
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  $\angle C=90^\circ$ , and  $A_0$ ,  $B_0$ ,  $C_0$  be the mid-points of sides  $BC$ ,  $CA$ ,  $AB$  respectively. Two regular triangles  $AB_0C_1$  and  $BA_0C_2$  are constructed outside  $ABC$ . Find the angle  $C_0C_1C_2$ .

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