
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 an isosceles triangle \(ABC\) with a right angle at \(C\), let \(P\) be an arbitrary point on side \(BC\), and let \(G\) denote the perpendicular projection of point \(C\) onto \(AP\). Let \(H\) be the point on segment \(AP\) such that \(AH = CG\). At what angle is segment \(GH\) viewed from the midpoint of \(AB\)?

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