
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
Pyramid $OABCD$ has a rectangular base $ABCD$ where $AB = 2BC$. All edges $\overline{OA}, \overline{OB}$, $\overline{OC}$, and $\overline{OD}$ are congruent, and $\angle AOB = 60^\circ$. Let $\theta$ be the measure of the dihedral angle formed by the faces $OAB$ and $OBC$. Find $\theta$ assuming $\cos \theta = m + \sqrt{n}$ where $m$ and $n$ are integers.

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