
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 sphere made of oil is floating in deep space. For what diameter will the total pressure at the center of the sphere, resulting from gravity and surface tension, be minimized? (The density of the oil is $0.8 \mathrm{~g} / \mathrm{cm}^{3}$ and its surface tension is $\alpha=30$ dyn $/ \mathrm{cm}$.)

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