
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 four propositions:
① A prism whose lateral faces are all congruent quadrilaterals must be a right prism;
② A hexahedron with congruent rectangular opposite faces must be a rectangular prism;
③ A prism with two lateral faces perpendicular to the base must be a right prism;
④ A rectangular prism must be a regular quadrilateral prism.
Determine the number of correct propositions.

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