
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 liquid \( X \) is insoluble in water. When poured into water, it forms a circular film of thickness \( 0.1 \mathrm{~cm} \) on the water surface unless stirred. If a rectangular container with dimensions \( 6 \mathrm{~cm} \), \( 3 \mathrm{~cm} \), and \( 12 \mathrm{~cm} \) is filled with liquid \( X \) and this liquid is poured onto a large water surface, calculate the radius of the resulting circular film.

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