
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
For the complex number $z = (1-i)a^2 - 3a + 2 + i$ ($a \in \mathbb{R}$),

(1) If $z = \bar{z}$, find $|z|$;

(2) If the point corresponding to the complex number $z$ in the complex plane is in the first quadrant, find the range of $a$.

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