
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 inequality $\frac{x+2}{k} > 1 + \frac{x-3}{k^{2}}$ for $x$, where $k \in \mathbf{R}$ and $k \neq 0$:
1. Solve this inequality.
2. If the solution set for this inequality is $(3, +\infty)$, find the value of $k$.
3. If $x=3$ is a solution to this inequality, find the value of $k$.

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