
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
A rectangular container measuring $8\, \text{cm}$ by $4\, \text{cm}$ by $10\, \text{cm}$ is filled with a liquid $Y$ that does not mix with water. When poured into a large body of water, it forms a circular film of thickness $0.05$ cm on the surface. Find the radius, in centimeters, of the resulting circular film.

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