
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 in the plane of triangle $ABC$ but outside the actual triangular region $ABC$. Denote by $s$ the sum of the distances from $E$ to the planes $DAB$, $DBC$, and $DCA$, and by $S$ the sum of the distances from $E$ to the lines $AB$, $BC$, and $CA$. Compute the ratio $\frac{s}{S}$.
A) $\frac{1}{\sqrt{2}}$
B) $\sqrt{2}$
C) $\frac{3\sqrt{2}}{2}$
D) $2$

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