
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 a modified game similar to Deal or No Deal, participants choose a box at random from a set of 30 boxes, each containing one of the following values: 
\begin{tabular}{|c|c|}
\hline
\$0.50 & \$2,000 \\
\hline
\$2 & \$10,000 \\
\hline
\$10 & \$20,000 \\
\hline
\$20 & \$40,000 \\
\hline
\$50 & \$100,000 \\
\hline
\$100 & \$200,000 \\
\hline
\$500 & \$400,000 \\
\hline
\$1,000 & \$800,000 \\
\hline
\$1,500 & \$1,000,000 \\
\hline
\end{tabular}
After choosing a box, participants eliminate other boxes by opening them. What is the minimum number of boxes a participant needs to eliminate to have at least a 50% chance of holding a box containing at least \$200,000?

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