
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 $PQRST$ has a square base $QRST$, with congruent edges $\overline{PR}, \overline{PQ}, \overline{PS},$ and $\overline{PT},$ and $\angle RQT=60^\circ.$ Let $\phi$ be the measure of the dihedral angle formed by faces $PQR$ and $PQS.$ Given that $\cos \phi=a+\sqrt{b},$ where $a$ and $b$ are integers, find $a+b.$

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