
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 vertex $C$ of the base $ABCDEF$ and parallel to the median $BM$ of the lateral face $SAB$ and the apothem $SN$ of the lateral face $SAF$. The side of the base of the pyramid is 2, and the distance from vertex $S$ to the cutting plane is 1. Find the cosine of the angle between the plane of the cross-section and the plane of the base.

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