
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 sets $A=\{x|x^2-7x+10\leq0\}$, $B=\{x|x^2+ax+b<0\}$, and $A\cap B=\varnothing$, $A\cup B=\{x|x-3<4\leq2x\}$, write out the set $S=\{x|x=a+b\}$.

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