
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
Among the following four propositions: ① An isosceles triangle with base angles equal to half of the vertex angle must be a right triangle; ② Given the same length of material, forming a square or a circular field on the ground, the area of the circular field will be larger; ③ A polyhedron with 5 faces must be a pyramid with a square base; ④ Three non-coincident planes in space can divide the space into 4, 6, 7, or 8 parts. The correct proposition numbers are .

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