
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
In quadrilateral $PQRS$, $\angle{PSQ} = \angle{PRQ}$ and $\angle{PQR} = \angle{SRQ}$. Given that $PQ = 7$, $QR = 5$, and $PS = 9$, find the length of side $RS$, which can be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are relatively prime integers. Determine $p + q$.

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