
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 complex number $z=\frac{2}{-1+i}$, four propositions are provided: $p_{1}$: $|z|=2$, $p_{2}$: $z^{2}=2i$, $p_{3}$: the conjugate of $z$ is $1+i$, $p_{4}$: the imaginary part of $z$ is $-1$. Determine the true proposition(s).

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