
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 $\omega = (m^2 - 2m - 3) + (m^2 - m - 12)i$, where $m \in \mathbb{R}$ and $i$ is the imaginary unit,

(1) If $\omega$ is a real number, find the value of $m$;

(2) If the point corresponding to the complex number $\omega$ is in the fourth quadrant, determine the range of real values of $m$.

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