
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
$\triangle ABC$ is inscribed in a circle of radius $r$ such that its base $AB$ coincides with the diameter $AB$. Point $C$ lies somewhere on the circle different from points $A$ and $B$. Let $s = AC + BC$. Determine the maximum possible value of $s^2$ given all permissible positions of $C$ on the circle.

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