
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 function $f(x)=ax^{2}+(b-2)x+3(a\neq 0)$,
(1) If the solution set of the inequality $f(x) > 0$ is $(-1,3)$. Find the values of $a$ and $b$;
(2) If $f(1)=2$, $a > 0$, $b > 0$, find the minimum value of $\frac {1}{a}+ \frac {4}{b}$.

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