
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
Here are four propositions about a tetrahedron:
① A tetrahedron with an equilateral triangle as the base and equal dihedral angles between the lateral faces and the base is a regular tetrahedron.
② A tetrahedron with an equilateral triangle as the base and all lateral faces being isosceles triangles is a regular tetrahedron.
③ A tetrahedron with an equilateral triangle as the base and all lateral faces having equal areas is a regular tetrahedron.
④ A tetrahedron with all lateral edges forming equal angles with the base, and equal dihedral angles between the lateral faces and the base is a regular tetrahedron.
Among these, the true propositions are $\boxed{\text{①④}}$. (Write down the numbers of all true propositions)

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