
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 acute-angled, nonisosceles triangle. Altitudes  $AA'$  and  $BB' $ meet at point  $H$ , and the medians of triangle  $AHB$  meet at point  $M$ . Line  $CM$  bisects segment  $A'B'$ . Find angle  $C$ .

(D. Krekov) 

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