
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
Two rats are drilling through a wall 1000 feet thick from opposite sides. The large rat drills one foot on the first day, while the small rat also drills one foot on the first day. Every day thereafter, the large rat's drilling speed doubles and the small rat's drilling speed halves. How many days will it take for the two rats to meet, rounded to the nearest whole number?

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