
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 base of the pyramid is a regular hexagon ABCDEF, and its side edge SA is perpendicular to the base plane. The distances from points B and C to the line SD are $\sqrt{\frac{23}{14}}$ and $\sqrt{\frac{15}{14}}$ respectively. 

a) What is the area of triangle ASD?

b) Find the ratio of the smallest area of the triangular sections of the pyramid passing through edge $SD$ to the area of triangle $ASD$?

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