
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 that the solution set of the inequality $x^2-x-6<0$ is $A$, and the solution set of the inequality $x^2-5x+4<0$ is $B$, find the value of $a-b$ for the inequality $x^2+ax+b<0$, where $A \cap B$ is the solution set.

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