
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
Given a cube $A B C D A 1 B 1 C 1 D 1$ with edge length $a$. On the rays $C 1 C$, $C 1 B 1$, and $C 1 D 1$, segments $C 1 M$, $C 1 N$, and $C 1 K$ are respectively laid out, each equal to $\frac{5}{2} a$. Construct the section of this cube by the plane passing through points $M$, $N$, and $K$, and find the area of the resulting section.

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