
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 version of Deal or No Deal, participants select a box from a set of 30 boxes, each containing a unique amount from this list:
\[
\begin{array}{|c|c|}
\hline
\$0.50 & \$800 \\
\hline
\$2 & \$1,500 \\
\hline
\$10 & \$3,000 \\
\hline
\$20 & \$10,000 \\
\hline
\$40 & \$25,000 \\
\hline
\$60 & \$50,000 \\
\hline
\$80 & \$75,000 \\
\hline
\$100 & \$100,000 \\
\hline
\$200 & \$200,000 \\
\hline
\$300 & \$300,000 \\
\hline
\$400 & \$400,000 \\
\hline
\$500 & \$500,000 \\
\hline
\$750 & \$750,000 \\
\hline
\$1,000 & \$1,000,000 \\
\hline
\end{array}
\]
What is the minimum number of boxes a participant needs to eliminate to have at least a 50% chance of holding a box with a value of \$75,000 or more?

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