
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 an isosceles triangle \(ABC\) where \(AB = AC\) and \(\angle BAD = 30^{\circ}\), \(D\) is an interior point on side \(BC\). Furthermore, triangle \(ADE\) is also isosceles, where \(E\) is an interior point on side \(AC\). What is the measure of \(\angle EDC\)?

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