
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

The chord $AB$ of a circle with radius 1 and center at $O$ is the diameter of a semicircle $ACB$ located outside the first circle. It is clear that the point $C$ of this semicircle, which protrudes the furthest, lies on the radius $ODC$ perpendicular to $AB$. Determine $AB$ so that the segment $OC$ has the maximum length.

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