
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
Let the universal set $I=\mathbb{R}$, $A=\{x|x^2-2x>0, x\in\mathbb{R}\}$, $B=\{x|x^2-ax+b<0, x\in\mathbb{R}\}$, $C=\{x|x^3+x^2+x=0, x\in\mathbb{R}\}$. Also, $\complement_{\mathbb{R}}(A\cup B)=C$, $A\cap B=\{x|2<x<4, x\in\mathbb{R}\}$. Find the values of $a$ and $b$.

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