
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 the complex number $(m^{2}-5m+6)+(m^{2}-3m)i$, where $m \in \mathbb{R}$ and $i$ is the imaginary unit,

$(1)$ For what value(s) of the real number $m$ is this complex number a real number;

$(2)$ For what value(s) of the real number $m$ is this complex number a pure imaginary number.

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