
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 the following propositions:
① If $z \in \mathbb{C}$, then $z^2 \geq 0$
② If $a, b \in \mathbb{R}$, and $a > b$, then $a+i > b+i$
③ If $a \in \mathbb{R}$, then $(a+1)i$ is a pure imaginary number
④ If $z= \frac{1}{i}$, then the point corresponding to $z^3+1$ is in the first quadrant of the complex plane
Among these propositions, the correct ones are __________. (Write down the numbers of all propositions you think are correct)

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