
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
Consider an isosceles triangle $ABC$ with $AB = AC = b$ and $BC = a$, where $b \geq a$. Let $P$ be the centroid of triangle $ABC$. Lines are drawn from $P$ through the vertices $A$, $B$, and $C$, meeting the opposite sides in $A'$, $B'$, and $C'$ respectively. Compute the sum $s = AA' + BB' + CC'$.

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