
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 of Deal or No Deal, participants choose a box at random from a set of 30 boxes, each containing one of the following values:
\[
\begin{tabular}{|c|c|}
\hline
\$0.05 & \$500 \\
\hline
\$2 & \$1,000 \\
\hline
\$10 & \$2,000 \\
\hline
\$20 & \$5,000 \\
\hline
\$50 & \$10,000 \\
\hline
\$75 & \$20,000 \\
\hline
\$100 & \$50,000 \\
\hline
\$150 & \$75,000 \\
\hline
\$200 & \$100,000 \\
\hline
\$250 & \$200,000 \\
\hline
\$300 & \$300,000 \\
\hline
\$350 & \$400,000 \\
\hline
\$400 & \$500,000 \\
\hline
\$450 & \$750,000 \\
\hline
\$500 & \$1,000,000 \\
\hline
\end{tabular}
\]
Determine the minimum number of boxes a participant needs to eliminate in order to have a one-third chance of holding at least \$75,000 as their chosen box.

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