
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
"In a triangle, the three medians intersect at one point, and the distance from this point to a vertex is twice the distance from it to the midpoint of the opposite side." By analogy: in a tetrahedron, the four medians (the line segments from a vertex to the centroid of the opposite face) intersect at one point, and the distance from this point to a vertex is equal to $\_\_\_$ times the distance from it to the centroid of the opposite face.

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