
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 values for the real number $m$.

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