
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 radius of the base of a cone is \( R \), and the angle between the slant height and the base plane is \( \alpha \). A sphere is inscribed in this cone. A tangent line is drawn through a point \( P \) on the circle of contact between the sphere and the cone. A plane is then drawn through this tangent line, parallel to the slant height of the cone that passes through the point diametrically opposite to \( P \). Find the area of the cross-section of the sphere made by this plane.

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