
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
For what values of the real number $m$ does the complex number $z=(m^{2}-8m+15)+(m^{2}+3m-28)i$ correspond to a point in the complex plane that:  
$(1)$ is in the fourth quadrant;  
$(2)$ is on the negative half of the $x$-axis;  
$(3)$ is in the upper half-plane (including the real axis).

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