
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 select a box at random from a set of $16$, each containing one of the following values: \begin{table}[ht]
\centering
\begin{tabular}{|c|c|}
\hline
$\$10$ & $\$50,000$ \\
\hline
$\$50$ & $\$75,000$ \\
\hline
$\$100$ & $\$200,000$ \\
\hline
$\$500$ & $\$400,000$ \\
\hline
$\$1,000$ & $\$500,000$ \\
\hline
$\$5,000$ & $\$1,000,000$ \\
\hline
\end{tabular}
\end{table}
After selecting a box, participants eliminate other boxes by revealing their contents to the audience, thereby removing the amount from play. Determine the minimum number of boxes a participant needs to eliminate to have at least a 50% chance of holding a box valued at least $\$500,000$.

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