
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
You are provided with two separate isosceles triangles, $ABC$ and $DEF$. The triangles are positioned so that point $C$ is at some distance directly to the right of point $F$ on the same horizontal level. If $\angle ABC = \angle ACB = 50^\circ$ and $\angle DEF = \angle DFE = 55^\circ$, then by extending side $AB$ it meets extended side $DE$ at a point $G$. Find the measure of $\angle CGE$.

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