
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 $A=\{x|(x^2+ax+b)(x-1)=0\}$, and set $B$ satisfies the condition $A \cap B = \{1, 2\}$, and $A \cap (C_U B) = \{3\}$, where $U=\mathbb{R}$, determine the value of $a+b$.

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