
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In the game Deal or No Deal, participants choose a box at random from a set of $26,$ one containing each of the following values: 
\begin{tabular}{|c|c|}\hline
\$.01&\$1,000\\\hline
\$1&\$5,000\\\hline
\$5&\$10,000\\\hline
\$10&\$25,000\\\hline
\$25&\$50,000\\\hline
\$50&\$75,000\\\hline
\$75&\$100,000\\\hline
\$100&\$200,000\\\hline
\$200&\$300,000\\\hline
\$300&\$400,000\\\hline
\$400&\$500,000\\\hline
\$500&\$750,000\\\hline
\$750&\$1,000,000\\\hline
\end{tabular} 
After choosing a box, participants eliminate other boxes by opening them, showing the amount of money in the box to the crowd, and then removing that box (and its money!) from the game. What is the minimum number of boxes a participant needs to eliminate in order to have a one-third chance of holding at least $\$250,000$ as his or her chosen box?

Present the answer in LaTex format: \boxed{Your answer}
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