
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
Triangle $PQR$ has vertices at $P(-1,2)$, $Q(5,4)$, and $R(4,-3)$. The point $S$ with coordinates $(m,n)$ is positioned inside the triangle such that the three smaller triangles $PQS$, $PRS$, and $QRS$ each have equal areas. Compute the value of $10m+n$.

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