
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 $f(x)=\frac{kx}{x^2+3k}$, where $k>0$.
(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 $k$.

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