
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 globe of chocolate sauce with a radius of 3 inches is placed in a bowl. As it melts due to the warmth of the room, the sauce forms a cylindrical puddle with a radius of 10 inches on the plate. Assuming the sauce's density stays the same, determine how many inches deep the melted sauce is. Express your answer as a common fraction.

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