
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
Circles \( C_1, C_2, C_3 \) have radius 1 and centers \( O, P, Q \) respectively. \( C_1 \) and \( C_2 \) intersect at \( A \), \( C_2 \) and \( C_3 \) intersect at \( B \), \( C_3 \) and \( C_1 \) intersect at \( C \), in such a way that \( \angle A P B = 60^\circ \), \( \angle B Q C = 36^\circ \), and \( \angle C O A = 72^\circ \). Find angle \( A B C \) (degrees).

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