
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
The angles \( A O B, B O C \), and \( C O D \) are equal to each other, and the angle \( A O D \) is three times smaller than each of them. All rays \( \mathrm{OA}, \mathrm{OB}, \mathrm{OC}, \mathrm{OD} \) are distinct. Find the measure of the angle \( A O D \) (list all possible values).

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