
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 the complex number $Z = (m^2 + 3m - 4) + (m^2 - 10m + 9)i$ where $m \in \mathbb{R}$,
1. Calculate the modulus of the complex number $Z$ when $m=0$.
2. For what values of the real number $m$ is the complex number $Z$ purely imaginary?
3. For what values of the real number $m$ does the point corresponding to the complex number $Z$ lie in the second quadrant of the complex plane?

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