
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
Liquid $Y$ does not mix with water and forms a circular film $0.2$cm thick when poured onto the surface of water. The volume of a rectangular box with dimensions $10$cm by $5$cm by $8$cm is $10\times 5\times 8 = 400$ cubic centimeters. Find the radius, in centimeters, of the resulting circular film.

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