
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 with edge length $a$, and let $E$ be a point inside triangle $ABC$. If $s$ is the sum of the distances from $E$ to the planes $DAB$, $DBC$, and $DCA$, and $S$ is the sum of the distances from $E$ to the lines $AB$, $BC$, and $CA$, evaluate the ratio $\frac{s}{S}$.

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