
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 triangle $DEF$, it is given that $DE = DF$ and point $G$ is on $EF$ such that $EG = GF$. If $\angle EDF = 2x$ and $DG$ is the bisector of $\angle EDF$, find the angle $\angle EGD$.
A) $72^\circ$
B) $90^\circ$
C) $108^\circ$
D) $120^\circ$

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