
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
Simplify the expression: 

\[
\frac{\sqrt{x^{2} y^{-2}-x y^{-1}+\frac{1}{4}} \cdot\left(x y^{-2}+y^{-3 / 2}\right)}{2 x^{2}-y^{3 / 2}-x y+2 x y^{1 / 2}}
\]

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