
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
Inside angle \( AOB \), which is \( 120^{\circ} \), rays \( OC \) and \( OD \) are drawn such that each of them bisects one of the angles formed by the initial drawing. Find the measure of angle \( AOC \), indicating all possible values.

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