
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 $MNP$, the medians $\overline{MQ}$ and $\overline{NR}$ have lengths $15$ and $20$, respectively, and $MN=30$. Extend $\overline{NR}$ to intersect the circumcircle of $MNP$ at $S$. Calculate the area of triangle $MSQ$ given that the resulting $m\sqrt{n}$, where $m$ and $n$ are positive integers, with $n$ not divisible by the square of any prime.

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