
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 \( \triangle ABC \) be a triangle with \(BA > BC\). Let \( M \) be the midpoint of \( AC \), and the internal bisector of angle \( \widehat{B} \) intersects \( AC \) at \( I \). The line parallel to \( BC \) passing through \( I \) intersects \( AM \) at \( E \). The line parallel to \( BA \) passing through \( M \) intersects \( AI \) at \( D \). What is the measure of the angle \( \widehat{EDI} \)?

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