
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
(1) Given that the solution set of the inequality $ax^2+2x+c>0$ is $\left\{x\middle| -\frac{1}{3}<x<\frac{1}{2}\right\}$, solve the inequality $cx^2-2x+a<0$.
(2) Given that the inequality $x^2-mx+4>0$ holds true for all $x>0$, determine the range of values for $m$.

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