
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 cross-section of a regular hexagonal pyramid SABCDEF is formed by a plane passing through the center of the base ABCDEF and parallel to the median CM of the lateral face SCD and the apothem SN of the lateral face SAF. The side of the base of the pyramid is 8, and the distance from the vertex S to the cutting plane is \(3 \sqrt{\frac{13}{7}}\). Find the cosine of the angle between the cutting plane and the base plane. (20 points)

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