
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 that the solution set of the inequality $ax^2+x+c>0$ is $\{x|1<x<3\}$.
(I) Find the values of $a$ and $c$;
(II) If " $ax^2+2x+4c>0$ " is a sufficient but not necessary condition for " $x+m>0$ ", find the range of the real number $m$.

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