
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 square base $ABCD$, where 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 between faces $OAB$ and $OBC$. Find $\cos \theta$ in the form $m-\sqrt{n}$, where $m$ and $n$ are integers, and determine $m+n.$

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