
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 side length \(s\), congruent edges \(\overline{PR}\), \(\overline{PQ}\), \(\overline{PS}\), and \(\overline{PT}\), and \(\angle QRT = 45^\circ\). 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}
user