
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
Square $ABCD$ has sides of length 5. Line segment $CP$ bisects diagonal $AC$, and line segment $CQ$ bisects side $CD$. Find the length of segment $CP$.
A) $\frac{5}{2}$
B) $\frac{5\sqrt{3}}{2}$
C) $5$
D) $\frac{5\sqrt{2}}{2}$
E) $\frac{7\sqrt{2}}{2}$

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