
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 a triangle with  $AC\neq BC$ , and let  $A^{\prime }B^{\prime }C$  be a triangle obtained from  $ABC$  after some rotation centered at  $C$ . Let  $M,E,F$  be the midpoints of the segments  $BA^{\prime },AC$  and  $CB^{\prime }$   respectively. If  $EM=FM$ , find  $\widehat{EMF}$ .

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