
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:  
$(1) {(-1)^{2020}}+{(-\frac{1}{2})^{-2}}-{(3.14-\pi)^0}$;  
$(2) 2x\cdot (3x^{2}-4x+1)$;  
$(3) (\frac{2}{3}{a^4}{b^7}-\frac{1}{9}{a^2}{b^6})÷(-\frac{1}{3}a{b^3})$;  
$(4) \left(x-2y\right)\left(x+2y\right)-\left(2x-y\right)^{2}$.

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