
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 \( O \) be the center of the circumcircle of \( \triangle ABC \). \( P \) and \( Q \) are the midpoints of \( AO \) and \( BC \), respectively. Suppose \( \angle CBA = 4 \angle OPQ \) and \( \angle ACB = 6 \angle OPQ \). Find the size of \( \angle OPQ \) in degrees.

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