
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
What is the value of the following expression:

$$
(4-x) \sqrt{x} \cdot \sqrt[3]{x-1} \cdot \sqrt[6]{2 x-\frac{1}{2}}
$$

for $x_{1}=2+\sqrt{3}$, and what is it for $x_{2}=2-\sqrt{3}$?

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