
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 $z = m^2 - m - 6 + (m^2 + 5m + 6)i$, where $m \in \mathbb{R}$ and $i$ is the imaginary unit,
1. If the complex number $z$ is purely imaginary, find the value of the real number $m$;
2. If the point corresponding to the complex number $z$ is in the second quadrant of the complex plane, find the range of values for the real number $m$.

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