
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
Let $XYZWV$ be a pentagon inscribed in a circle such that $XZ = ZV = 4$, $ZW = WV = 9$, and $XV= 13$. The sum of the lengths of all diagonals of $XYZWV$ is equal to $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. What is $p+q$?

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