
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 right prism \(A B C A_{1} B_{1} C_{1}\) is a triangle \(A B C\) with angle \(B\) equal to \(90^{\circ}\) and angle \(C\) equal to \(30^{\circ}\). Find the area of the cross-section of the prism by a plane passing through the center of the lateral face \(A A_{1} C_{1} C\) and the vertex \(B\) and parallel to the diagonal of the lateral face \(A B_{1}\), given that the distance from vertex \(C\) to the cutting plane is 2 and the hypotenuse of the base of the prism is 4.

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