
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
The lateral face of a regular quadrilateral pyramid forms a $45^\circ$ angle with the plane of the base. Find the angle between the slant height (apotheme) of the pyramid and the plane of an adjacent face.

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