
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 lateral edge of a regular triangular pyramid is inclined to the base plane at an angle of $45^{\circ}$. Find the side of the base if the volume of the pyramid is 18.

In a regular triangular prism $A B C A_1 B_1 C_1$, a cross-section is made by a plane passing through the midpoint $M$ of edge $A B$, point $B_1$, and point $K$ lying on edge $A C$ and dividing it in the ratio $A K: K C = 1: 3$. Find the area of the cross-section if the side of the base of the prism is $a$, and the height of the prism is $2a$.

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