
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 \( ABC \) be an isosceles triangle with \( A \) as the vertex angle. Let \( M \) be the midpoint of the segment \( [BC] \). Let \( D \) be the reflection of point \( M \) over the segment \( [AC] \). Let \( x \) be the angle \( \widehat{BAC} \). Determine, as a function of \( x \), the value of the angle \( \widehat{MDC} \).

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