
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 $350 \mathrm{~cm}^{3}$ volume iron cone, whose height is equal to its base radius, is floating upside down in mercury. How deep does this cone submerge in the mercury, given that the specific gravity of the iron is $7.2 \mathrm{g/cm}^3$ and the specific gravity of the mercury is $13.6 \mathrm{g/cm}^3$?

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