
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 base of pyramid \( TABC \) is a triangle \( ABC \) with all sides equal to \(\sqrt{3}\), and the height of the pyramid coincides with the lateral edge \( TA \). Find the area of the cross-section of the pyramid by a plane that passes through the center of the circumscribed sphere around the pyramid, forms an angle of \(60^\circ\) with the base plane, intersects the edge \( AB \) at point \( M \) such that \( MB = 2AM \), and intersects the edge \( BC \). It is given that the distance from point \( A \) to the plane of the cross-section is 0.25.

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