
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 $\overline{PQ}, \overline{PR}, \overline{PS},$ and $\overline{PT},$ and $\angle QRP=45^\circ.$ Let $\phi$ be the measure of the dihedral angle formed by faces $PQR$ and $PRS.$ Given that $\cos \phi = x+\sqrt{y},$ where $x$ and $y$ are integers, find $x+y.$

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