
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 long, light cylinder has an elliptical cross-section with semi-axes \(a > b\). It lies on the ground with its main axis horizontal and the major axes horizontal. A thin heavy wire of the same length as the cylinder is attached to the line along the top of the cylinder. For what values of \(b/a\) is the cylinder in stable equilibrium?

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