
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
A box contains three shiny new coins and four tarnished old coins. Coins are drawn randomly one by one without replacement from the box. Find the probability that it takes more than 4 draws to remove all the new coins.

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