
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 a rectangle $ABCD$ with sides $AB = l$ and $BC = w$, where $l \geq w$. A point $P$ is anywhere inside the rectangle. Lines from $P$ meet the extensions of sides $AB$, $BC$, $CD$, and $DA$ at points $E$, $F$, $G$, and $H$, respectively. Let $s = PE + PF + PG + PH$. Determine the maximum possible value of $s$ given the configuration.
A) $l + w$
B) $2l$
C) $2w$
D) $2l + 2w$
E) $l + 2w$

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