
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 $z=(m^{2}-8m+15)+(m^{2}-9m+18)i$, which is represented by point $A$ in the complex plane, find the values of the real number $m$ such that:
1. $z$ is a real number?
2. $z$ is a purely imaginary number?
3. $A$ is located in the third quadrant?

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