
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
Let $m \in \mathbb{R}$, and the complex number $z = (2+i)m^2 - 3(1+i)m - 2(1-i)$.  
(1) If $z$ is a real number, then $m = \boxed{\text{1 or 2}}$;  
(2) If $z$ is a pure imaginary number, then $m = \boxed{-\frac{1}{2}}$.

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