
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
Given a chord in a circle, we inscribe a circle with the largest possible radius in the larger of the two segments created by the chord. What choice of the chord length will result in the segment outside the inscribed circle having the largest area?

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