
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 function $f(x) = mx^{2} - nx$ where $m, n \in \mathbb{R}$.  
$(1)$ If the solution set of the inequality $f(x) \geq t$ where $t \in \mathbb{R}$ is $\{x | -3 \leq x \leq 2\}$, find the solution set of the inequality $nx^{2} + mx + t \leq 0$.  
$(2)$ If $f(1) > 0$ and $m \in [1,3]$, find the minimum value of $\frac{1}{m-n} + \frac{9}{m} - n$.

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