
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 and then evaluate it: $5x^2y - [6xy - 2(xy - 2x^2y) - xy^2] + 4xy$, where $x$ and $y$ satisfy $|x + \frac{1}{2}| + (y - 1)^2 = 0$.

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