
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 solution set of the inequality $x^2-4x+3<0$ be $A$, and the solution set of the inequality $x^2+x-6>0$ be $B$.

(1) Find $A \cap B$;  
(2) If the solution set of the inequality $x^2+ax+b<0$ is $A \cap B$, find the values of $a$ and $b$.

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