
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
A pyramid $PQRS$ has a square base $QRSU$ and congruent edges $\overline{PQ}, \overline{PR}, \overline{PS},$ and $\overline{PU}$. The angle $\angle QPR = 45^\circ$. Let $\phi$ be the measure of the dihedral angle formed by faces $PQR$ and $PRS$. Given that $\cos \phi = a + \sqrt{b}$, find $a + b$.

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