
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
If two congruent circles centered at points $P$ and $Q$ each pass through the other circle's center, a line containing both $P$ and $Q$ is extended to intersect the circles at points $F$ and $G$, and the circles intersect at point $H$, where $\triangle PFQ$ is such that $PF = FQ$ and $PQ = QH = PH$, find the degree measure of $\angle FHG$.

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