
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
Let  $ABCDE$  be a regular pentagon, and let  $F$  be a point on  $\overline{AB}$  with  $\angle CDF=55^\circ$ .  Suppose  $\overline{FC}$  and  $\overline{BE}$  meet at  $G$ , and select  $H$  on the extension of  $\overline{CE}$  past  $E$  such that  $\angle DHE=\angle FDG$ . Find the measure of  $\angle GHD$ , in degrees.

*Proposed by David Stoner*

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