
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
By analogy with the property of an equilateral triangle in the plane, which has "all three sides equal, all three internal angles equal," we can infer some properties of a regular tetrahedron: "All edges are of equal length, the angle between any two edges at the same vertex is equal; All faces are congruent equilateral triangles, the dihedral angle between any two adjacent faces is equal; All faces are congruent equilateral triangles, the angle between any two edges at the same vertex is equal. Which do you think is more appropriate?

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