
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
Calculate and simplify the following expressions:<br/>$(1){(-4)}^{2}-6×\frac{4}{3}+2×{(-1)}^{3}÷(-\frac{1}{2})$;<br/>$(2)-{1}^{4}-\frac{1}{6}×|2-\left(-3\right)^{2}|$;<br/>$(3)$Given $|x+2|+\left(y-1\right)^{2}=0$, find the value of the polynomial $2(3x^{2}y+xy^{2})-3(2x^{2}y-xy)-2xy^{2}+1$.

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