
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 function $y=(m+3)x^{(m^{2}+3m-2)}$ is a quadratic function in terms of $x$.
$(1)$ Find the value of $m$;
$(2)$ For what value of $m$ does the graph of the function open downwards?
$(3)$ For what value of $m$ does the function have a minimum value?

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