
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 quadratic function $y=x^{2}+mx+m^{2}-3$ where $m$ is a constant and $m \gt 0$, and the graph passes through the point $P(2,4)$.
$(1)$ Find the value of $m$;
$(2)$ Determine the number of intersection points between the graph of the quadratic function $y=x^{2}+mx+m^{2}-3$ and the $x$-axis, and provide a reason.

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