
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 \(ABC\), \(AB\) is congruent to \(AC\), the measure of angle \(ABC\) is \(60^\circ\) and segment \(BD\) bisects angle \(ABC\) with point \(D\) on side \(AC\). If point \(E\) is on side \(BC\) such that segment \(DE\) is parallel to side \(AB\), and point \(F\) is on side \(AC\) such that segment \(EF\) is parallel to segment \(BD\), and point \(G\) is on side \(AB\) such that segment \(EG\) is parallel to side \(AC\), determine how many isosceles triangles are formed?

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