
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
$(1)\frac{1}{9}\sqrt{9}-\sqrt[3]{27}+\sqrt[3]{-64}+\sqrt{(-\frac{1}{2})^{2}}$；<br/>$(2)(4x^{2}y-8xy^{2}+4xy)\div \left(-2xy\right)$；<br/>$(3)\left(2x+3\right)\left(3x-2\right)$；<br/>$(4)\left(3x-y\right)^{2}-\left(3x+2y\right)\left(3x-2y\right)$.

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