
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 box contains one of the following values, each appearing once: $0.01, 1, 5, 10, 25, 50, 100, 200, 300, 400, 500, 750, 1,000, 5,000, 10,000, 25,000, 50,000, 75,000, 100,000, 200,000, 300,000, 400,000, 500,000, 750,000, 1,000,000$. A participant wants to have a half chance of holding a box containing at least $200,000$. What is the minimum number of boxes they need to eliminate?

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