
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 the game Deal or No Deal, participants choose a box at random from a set of $30,$ one containing each following values: the same as provided in the initial problem with the addition of four boxes containing $5,500$, $6,600$, $7,700$, and $8,800$. After choosing a box, participants eliminate other boxes by opening them and then remove that box from play. What is the minimum number of boxes a participant needs to eliminate to have a one-third chance of holding at least $75,000$ in his or her chosen box?

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