
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
Given a regular tetrahedron $ABCD$, consider a point $E$ inside the tetrahedron. Define $t$ as the sum of the distances from $E$ to the vertices $A$, $B$, $C$, and $D$. Compute the ratio $t/V$, where $V$ is the volume of the tetrahedron $ABCD$.
A) $\frac{\sqrt{3}}{s^2}$
B) $\frac{6 \sqrt{3}}{s^2}$
C) $\frac{12 \sqrt{3}}{s^2}$
D) $\frac{3 \sqrt{3}}{s^2}$
E) $\frac{9 \sqrt{3}}{s^2}$

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