
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 inequality $|x^{2}-3x-4| < 2x+2$, the solution set is denoted as ${x|a < x < b}$.

1. Find the values of $a$ and $b$.
2. If $m$, $n∈(-1,1)$, and $mn= \frac {a}{b}$, $S= \frac {a}{m^{2}-1}+ \frac {b}{3(n^{2}-1)}$, find the maximum value of $S$.

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