
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 \(ABC\), all sides of which are equal to 3, and the height of the pyramid, equal to \(\sqrt{3}\), 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 of the pyramid, is parallel to the median \(AD\) of the base, and forms an angle of \(60^{\circ}\) with the base plane.

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