
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 $U = \mathbb{R}$, let the set A be defined by $\{ x | x < -4 \text{ or } x > 1 \}$, and the set B be defined by $\{ x | -3 \leq x - 1 \leq 2 \}$. Find $A \cap B$ and $(\complement_U A) \cup (\complement_U B)$.
2. Evaluate the following expression, given that $x > 0$: 
$$(2x^{\frac{1}{4}} + 3^{\frac{3}{2}})(2x^{\frac{1}{4}} - 3^{\frac{3}{2}}) - 4x^{-\frac{1}{2}}(x - x^{\frac{1}{2}}).$$

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