
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 sphere touches the base plane $ABCD$ of a regular quadrangular pyramid $SABCD$ at point $A$ and also touches the inscribed sphere of the pyramid. A secant plane is drawn through the center of the first sphere and the side $BC$ of the base. Find the angle of inclination of this plane to the base plane, given that the diagonals of the section are perpendicular to the edges $SA$ and $SD$.

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