
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 the apex at $A$. Let $M$ be the midpoint of segment $[BC]$. Let $D$ be the symmetric point of $M$ with respect to 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}
user