
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 the complex number $z$($= \frac{2}{-1+i}$): $(①)$:$|z|=2$; $(②)$:$z^{2}=2i$; $(③)$: the imaginary part of $z$ is $(-1)$; $(④)$: the conjugate of $z$ is $(1+i)$. The true proposition(s) is/are ________.

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