
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 spherical scoop of chocolate ice cream with a radius of 3 inches is dropped onto the surface of a dish of warm caramel sauce. As it melts, the ice cream spreads out uniformly forming a cylindrical region 12 inches in radius. Assuming the density of the ice cream remains constant, how many inches deep is the melted ice cream? Express your answer as a common fraction.

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