
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 square base  $ABCD,$  congruent edges  $\overline{OA}, \overline{OB}, \overline{OC},$  and  $\overline{OD},$  and  $\angle AOB=45^\circ.$   Let  $\theta$  be the measure of the dihedral angle formed by faces  $OAB$  and  $OBC.$   Given that  $\cos \theta=m+\sqrt{n},$  where  $m$  and  $n$  are integers, find  $m+n.$ 

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