
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 triangle $XYZ$, $G$ and $H$ are the midpoints of $\overline{XY}$ and $\overline{YZ}$ respectively. If $X=(0,8)$, $Y=(0,0)$, and $Z=(10,0)$, find the sum of the $x$ and $y$ coordinates of $J$, the point of intersection of $\overline{XH}$ and $\overline{YG}$.

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