
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
$ABCD$ is a square with side length $s$. $P$ is any point on $\overline{AB}$. $\overline{PS} \perp \overline{BD}$, and $\overline{PR} \perp \overline{AC}$. $\overline{AF} \perp \overline{BD}$, and $F$ is the midpoint of $\overline{BD}$. If $\overline{PQ} \perp \overline{AF}$, find $PR + PS$.
A) $s$
B) $\frac{s\sqrt{2}}{2}$
C) $s\sqrt{2}$
D) $2s$

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