
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