
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
The "Two Mice Through the Wall" problem from the "Nine Chapters on the Mathematical Art" is a classic problem in Chinese mathematics: "There is a wall of certain thickness. Two mice, one larger and one smaller, start to burrow through the wall from opposite sides. The larger mouse burrows 1 foot on the first day and doubles its distance each day thereafter. The smaller mouse also burrows 1 foot on the first day but halves its distance each day thereafter. If the wall is $64 \frac{31}{32}$ feet thick, __________ days later, the two mice will meet, having burrowed through the wall."

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