
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 a coordinate plane, triangle $XYZ$ has vertices at $X(-2, 8)$, $Y(0, 2)$, and $Z(6, 2)$. $M$ is the midpoint of $\overline{XY}$, and $N$ is the midpoint of $\overline{YZ}$. Find the product of the $x$ and $y$ coordinates of $P$, the point of intersection of $\overline{XM}$ and $\overline{ZN}$.

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