
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 distinct amounts of money ranging from $1 to $1,000,000, distributed as follows: $\$1, \$10, \$20, \$50, \$100, \$200, \$300, \$400, \$500, \$750, \$1,000, \$2,000, \$3,000, \$5,000, \$7,500, \$10,000, \$15,000, \$20,000, \$25,000, \$30,000, \$40,000, \$50,000, \$75,000, \$100,000, \$200,000, \$300,000, \$400,000, \$500,000, \$750,000, \$1,000,000$. What is the minimum number of boxes a participant needs to eliminate to have at least a 50% chance of holding a box with at least $50,000?

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