
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 cylindrical container with a radius of 5 cm and a height of 8 cm is completely filled with a non-water-soluble liquid. This liquid is poured onto a water surface where it forms a uniform film that is 0.2 cm thick. What is the radius, in centimeters, of the resulting circular film?
A) $100 \text{ cm}$  
B) $10\sqrt{10} \text{ cm}$  
C) $20\sqrt{5} \text{ cm}$  
D) $30 \text{ cm}$

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