
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
(1) Given the universal set $U=\mathbb{R}$, set $A=\{x\mid 1\leqslant x-1 < 3\}$, $B=\{x\mid 2x-9\geqslant 6-3x\}$. Find: (1-1) $A\cup B$; (1-2) $\complement_{U}(A\cap B)$
(2) Simplify: $(-2x^{\frac{1}{4}}y^{-\frac{1}{3}})(3x^{-\frac{1}{2}}y^{\frac{2}{3}})(-4x^{\frac{1}{4}}y^{\frac{2}{3}})$.

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