
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
Today, there is a wall that is 8 feet thick, and two mice are burrowing through it from both sides. The big mouse burrows 1 foot on the first day, and the small mouse burrows half a foot on the first day. Each day after, the big mouse burrows a length that is twice as long as the previous day, and the small mouse burrows a length that is half as long as the previous day. Determine the number of days it will take for the two mice to meet.

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