
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 $z = m^2\left(\frac{1}{m+8} + i\right) + (6m-16)i - \frac{m+2}{m+8}$, where $i$ 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 third or fourth quadrant, find the range of values for the real number $m$.

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