
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 \( ABC \) with all sides 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 sphere circumscribed around the pyramid, is parallel to the median \( AD \) of the base, and forms an angle of \( 60^\circ \) with the plane of the base.

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