
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
Consider triangle $XYZ$ with vertices at $X(-1,4)$, $Y(5,2)$, and $Z(3,10)$. Find the point $P$ with coordinates $(m,n)$ inside the triangle such that the three smaller triangles $XYP$, $XZP$, and $YZP$ all have equal areas. What is the value of $10m + n$?

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