
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
In a circle with center $O$ and radius $r$, let $AB$ be a chord smaller than the diameter. The radius of the inscribed circle in the smaller circular segment formed by the radii $AO$ and $BO$ is denoted by $\varrho$. Express $AB$ in terms of $r$ and $\varrho$.

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