
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
Let $ABCD$ be a regular tetrahedron, and let $E$ be a point lying exactly in the middle of edge $AB$. Denote $s$ as the sum of the distances from $E$ to the planes $DAC$, $DBC$, and the plane containing the face $BCD$, and $S$ as the sum of the distances from $E$ to the remaining edges $AC$, $BC$, $CD$, $DA$, and $DB$. Calculate $\frac{s}{S}$.
A) $\frac{9}{10}$  
B) $\frac{3}{2}$  
C) $1$  
D) $\frac{1}{3}$  
E) $\frac{\sqrt{2}}{2}$

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