
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 the diagram, \( G \) and \( H \) are the midpoints of \( \overline{PQ} \) and \( \overline{QR} \) respectively, where \( P(0,8) \), \( Q(0,0) \), and \( R(10,0) \). Find the sum of the \( x \) and \( y \) coordinates of \( I \), the point of intersection of \( \overline{PH} \) and \( \overline{GQ} \).

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