
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 the pyramid \(TABC\) is a triangle \(ABC\), where all sides are 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 sphere circumscribed around the pyramid, forms an angle of \(60^{\circ}\) with the plane of the base, intersects the edge \(AB\) at point \(M\) such that \(MB = 2AM\), and intersects the edge \(BC\). It is known 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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