
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 $\triangle ABC$ be a triangle with sides $a$, $b$, and $c$ such that $a \geq b \geq c$, find the maximum possible value of $s = AA' + BB' + CC'$ where $s = AA' + BB' + CC'$ and $AA'$, $BB'$, and $CC'$ are the perpendicular distances from point $P$ to the sides $BC$, $AC$, and $AB$.

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