
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 $f(x)=ax^2+x-a$, where $a \in \mathbb{R}$.

$(1)$ If the solution set of the inequality $f(x) < b$ is $(-\infty, -1) \cup (3, +\infty)$, find the values of $a$ and $b$.

$(2)$ If $a < 0$, solve the inequality $f(x) > 1$.

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