
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 $f(x) = \frac{kx}{x^2 + 3k}$ ($k > 0$).
1. If the solution set of $f(x) > m$ is $\{x | x < -3 \text{ or } x > -2\}$, find the solution set of the inequality $5mx^2 + \frac{k}{2}x + 3 > 0$.
2. If there exists $x > 3$ such that $f(x) > 1$, find the range of values for $k$.

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