
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 semicircle of radius $r$ with $AB$ as a diameter. Point $C$ lies above $AB$ forming a right angle at $C$. If $\theta$ is the angle at $C$ between $AC$ and a vertical line from $C$ to $AB$, and $s = AC + BC$, what is the maximum value of $s^2$?

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