
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 triangle $PQR$, the medians $\overline{PM}$ and $\overline{QN}$ have lengths $15$ and $20$, respectively, and $PQ=30$. Extend $\overline{QN}$ to intersect the circumcircle of $PQR$ at $S$. The area of triangle $PSR$ is $k\sqrt{l}$, where $k$ and $l$ are positive integers and $l$ is not divisible by the square of any prime. Find $k+l$.

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