
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
The following propositions:<br/>① The diagonals of a rectangle bisect each other and are equal;<br/>② A quadrilateral with equal diagonals is a rectangle;<br/>③ Each diagonal of a rhombus bisects a pair of angles;<br/>④ A parallelogram with one diagonal bisecting a pair of angles is a rhombus.<br/>Among them, the correct propositions are ______ (Note: Fill in the numbers of the propositions you think are correct).

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