
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 each edge length equal to 2 units. Let $P$ be a point inside the tetrahedron equidistant from all the vertices. Calculate the ratio of the sum of the distances from $P$ to each face of the tetrahedron ($s$) to the sum of the distances from $P$ to each edge of the tetrahedron ($S$).
A) $\frac{1}{\sqrt{2}}$
B) $\frac{1}{\sqrt{3}}$
C) $\frac{\sqrt{6}}{3}$
D) 2

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