
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
(14 points) Given the universal set $U=\mathbb{R}$, set $A=\{x|x-1\geq0\}$, $B=\{x|(x+1)(x-2)\leq0\}$.
(1) Find $A\cap B$
(2) Find $\complement_U(A\cup B)$

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