
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 a quadratic equation with real coefficients about $x$: $2x^2-4(m-1)x+m^2+1=0$.

(1) If the equation has roots $x_1$ and $x_2$, and $|x_1|+|x_2|=2$, find the value of $m$;  
(2) If the equation has a complex root $z$, and $z^3 \in \mathbb{R}$, find the value of $m$.

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