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

(1) Find $z$ if it is a pure imaginary number.

(2) Find the range of values of $a$ if the point corresponding to the complex number $z$ lies in the third quadrant of the complex plane.

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