
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 $z=(m^{2}-8m+15)+(m^{2}-9m+18)i$, for what values of the real number $m$ will:<br/>
$(1)$ the complex number $z$ be a real number;<br/>
$(2)$ the complex number $z$ be a pure imaginary number;<br/>
$(3)$ the point corresponding to the complex number $z$ be located in the third quadrant.

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