
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 set $A=\{x\mid x^2-2x-3>0\}$ and the set $B=\{x\mid ax^2+bx+c\leq0, a,b,c\in\mathbb{R}, ac\neq0\}$. If $A\cap B=(3,5]$ and $A\cup B=\mathbb{R}$, then the value of $\frac{b}{a}+\frac{a^2}{c^2}$ is ______.

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