
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 a complex number $z = m^2 + m - 2 + (2m^2 – m – 3)i$ where $m \in \mathbb{R}$, find the set of real numbers $m$ for which the point corresponding to the conjugate of $z$, denoted by $\bar{z}$, lies in the first quadrant.

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