
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
For each vertex of triangle  $ABC$ , the angle between the altitude and the bisectrix from this vertex was found. It occurred that these angle in vertices  $A$  and  $B$   were equal. Furthermore the angle in vertex  $C$  is greater than two remaining angles. Find angle  $C$  of the triangle.

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