
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
In space, from a point \( O \) four rays \( OA, OB, OC, \) and \( OD \) are drawn. If \( \angle AOB = \angle BOC = \angle COD = \angle DOA = \angle BOD = \angle AOC = \theta \), find the value of \( \theta \). (Express in terms of arccos).

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