
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 is inscribed in a regular quadrilateral pyramid \(MABCD\) with vertex \(M\). A second sphere touches the first sphere and the plane of the pyramid's base at point \(A\). A plane is drawn through the center of the second sphere and the side \(BC\) of the pyramid's base, intersecting edge \(MA\) at point \(K\). Find the angle of inclination of this plane to the plane of the base of the pyramid, given that edge \(MA\) and diagonal \(CK\) of the cross-section are perpendicular.

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