
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
Given that liquid $Y$ forms a circular film $0.2$ cm thick when poured onto a water surface, find the radius, in centimeters, of the resulting circular film created when a rectangular box with dimensions $10$ cm by $5$ cm by $20$ cm is filled with liquid $Y$ and its contents are poured onto a large body of water.

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