
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
Find the area of the cross-section of a regular triangular prism \( ABC A_1 B_1 C_1 \) by a plane that passes through the vertex \( C \) and the midpoint of the side \( B_1 C_1 \) of the base \( A_1 B_1 C_1 \) and is parallel to the diagonal \( AC_1 \) of the lateral face \( AA_1 C_1 C \). The distance between the line \( AC_1 \) and the cutting plane is 1, and the side of the base of the prism is \(\sqrt{14}\).

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