The plan was as such:

First, the Sinclair family would go greet King Leopold of Iridia, Nicholas's  father. Alexandra planned to use this opportunity to show off her "changed" personality and win the king's favor. If he liked her, she was less likely to suffer consequences for breaking off the engagement with Nicholas. 

After they greeted the king, Elias and their father would go off with him to do their jobs. While they did their thing, Alexandra would go find Nicholas. He would not be expecting her, since she tagged along with Elias and the Duke so last minute. Thus, he was almost certainly with another woman. According to the noble rumor mill, this week's lady was...some Marquis's daughter? Alex never bothered to learn the name. Instead, for ease of memory, she would be referring to the girl as Extra #1. Anyways, according to her information (maids' gossip) the two had been seen together a lot recently, so they should be together still. Once she had confirmed Nicholas's location and company, she would return to the king and her family. 

This was where Elias would come in. After Alexandra secretly told him the information, he would subtly guide the group to that location, citing a desire to learn. Since Eli was the heir to the duchy, the two older men would be more inclined to listen to them. Then, they would "accidentally" come across the prince and Extra #1. Using her amazing acting skills, honed by years of feigning sickness to skip classes and practice kendo, Alex would pretend to be shocked and devastated about her fiancé's betrayal and beg the king for an annulment due to her honor being tarnished in such a way. 

Alexandra smirked. This was a foolproof plan! After seeing his son's infidelity with his own eyes, King Leopold would have no choice but to allow the annulment, or risk losing the loyalty of the Sinclair house. After all, honor was paramount in this world, and any noble would be able to understand how unforgivable such an offense would be. For once, her father's obsession with titles and tradition would actually be helpful.

***

"Greetings, Your Majesty, King Leopold Aelius."

"Duke Edumnd Sinclair, you may rise."

As her father straightened up from his bow, Alexandra observed the country's monarch. King Leopold Aelius was a large, imposing man. His dark brown hair and beard gleamed in the light, and his piercing blue eyes seemed to look right through her. In all of Old Alexandra's past meetings with the man, he had seemed completely indifferent, if not a little averse, to her, regarding her brother and father with markedly more fondness. She was determined to change that mindset today. 

When the Duke waved his children forward, Alexandra lowered her eyes respectfully and dipped into a perfect curtsy.

"Lady Alexandra Sinclair, daughter of the Duke Sinclair, greets His Majesty King Leopold Aelius, the Sun of Iridia." This was the most formal way a person could address his or her superior, and by choosing this greeting, she was displaying the most respect she could. 

"Lord Elias Sinclair, son of the Duke Sinclair, greets His Majesty King Leopold Aelius, the Sun of Iridia," Elias followed suit. The king nodded back at Elias, but looked at Alexandra with a hint of interest in his eyes. She could understand why, she supposed, recalling Old Alexandra's memories of embarrassingly casual greetings because of the King's position as her future father-in-law.

"You may rise," the king acknowledged.

She did, but instead of immediately excusing herself to find Nicholas as Old Alexandra had in the past, she stayed quietly where she was. King Leopold took notice of that and turned to her, mild interest becoming curiosity. 

"Lady Alexandra, is there something you would like to ask of me?"

She shook her head slightly. "Only your forgiveness, sire."

He raised an eyebrow. "Oh? And what is this for?"

Alex dropped into a low curtsy, the picture of remorse. 

"Two weeks ago, my carriage overturned. Since that accident, I have had much time for introspection and have realized the weight of my behavior. Please forgive my past impudence."

King Leopold looked impressed.

"Rise, my child," he beckoned. "It requires a strong character to willingly reflect upon one's actions, and an even stronger one to admit one's faults and ask forgiveness. You are pardoned. Raise your head."

Alexandra met his gaze and smiled gratefully. "Thank you, my king."

Off to the side, she could see her father's barely-hidden shock and her brother's proud grin. With this one apology, she had risen in status by leaps and bounds in the eyes of the king. 

As everyone sat down and the men began to talk about general matters, Alex allowed herself to fade into the background, content to stay and display her "newfound patience" to the king. 

"...and the Church is beginning to ask for more and more funding. At this rate, we are going to have to impose heavier taxes to support this."

Her ears perked up at the new topic of conversation. This could be a chance to curry favor with the king. He seemed to be the kind of person who heavily favored more useful people. However, she would have to be careful about the way she presented her ideas. She couldn't afford to offend anyone.

She sat forward in her seat and waited for the king to notice her engagement in their conversation. He easily caught the movement and addressed her.

"Lady Alexandra? Do you have something to say?"

"My king," she spoke softly and calmly. "I was listening to the conversation, and the matter of the Church piqued my interest. If I may be so bold as to speak my thoughts?"

The Duke shot her a sharp glare clearly telling her to shut up, but King Leopold fixed her with an inquisitive stare and bade her continue.

"Thank you," she began to speak. "I believe that imposing heavier taxes on the people would lead to public dissent and areas of great poverty. Many of the commonfolk are barely getting by as it is. However, you cannot ignore the requests of the Church. So how would you acquire the necessary funds? My answer to this question is a tax on foreign goods."

"Oh?" The King sat forward in his seat curiously. "Please, continue."

"With your permission," she inclined her head. "Currently, foreign goods flow into our country without restriction. By levying a small tax on the sales of certain foreign goods, you could easily make up the funds without harming the livelihoods of the extremely poor in our kingdom. They cannot afford the foreign goods in the first place, so the tax would not affect them. There is an additional benefit to this tax. Since foreign goods would thus be more expensive, the people would spend more of their money on items produced here in Iridia. This would improve the circulation of money and ensure that more of our riches stay within our kingdom. The only disadvantage I see is that our exports to other kingdoms would suffer a little because other kingdoms would tax our products in return, but it is a small price to pay."

King Leopold nodded his head approvingly. "That is an excellent plan, Lady Alexandra. Might I ask where you got this idea?"

She smiled. "Thank you for your praise. The idea is of my own concoction. While I was bedridden from the accident, I had my maids bring me many books. I studied a lot about economics, and came up with this idea while I was doing so. I was going to talk to my father about implementing this idea in our fief, but I am happy that my thoughts were helpful to you."

The king smiled back. "You have truly become a bright child. I am thankful for your help. However, I must now ask you to go to your fiancé. We are going to discuss more delicate matters, and it would not do for you to sit in on those conversations."

Alex gracefully rose to her feet and curtsied. "It is my honor to be of service, my king. As per your advice, I will take my leave now. Thank you for your time."

Ignoring her father's expression of disbelief, she turned to Elias and smiled. 

"I will return when you have finished. I hope you have a frutiful meeting."

Rising to his feet as well, Elias offered her his arm. "Please, let me walk my sister to the door."

She took it. "Thank you, brother." She turned to the two older men, both of which were looking surprised at their good relationship. "Well then, I will bid you goodbye for now."

With that, the two siblings left the king's office.

As soon as the door shut behind them, they exchanged a gleeful high-five.

Step One of Operation Garbage Disposal was a success. 

Now for Step Two.