
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 $U=\mathbb{R}$, and sets $A=\{x\mid x < -4 \text{ or } x > 1\}$ and $B=\{x\mid -3 \leqslant x-1 \leqslant 2\}$, find $A \cap B$ and $(A^c \cup B^c)$;
(2) Evaluate: If $x > 0$, find $(2x^{ \frac {1}{4}}+3^{ \frac {3}{2}})(2x^{ \frac {1}{4}}-3^{ \frac {3}{2}})-4x^{- \frac {1}{2}}(x-x^{ \frac {1}{2}})$.

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