
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 the following:<br/>$(1){({-1})^{2023}}+{({π-3.14})^0}-{({-\frac{1}{2}})^{-2}}$;<br/>$(2)({\frac{1}{4}{x^4}+2{x^3}-4{x^2}})÷{({-2x})^2}$;<br/>$(3)\left(2x+y+1\right)\left(2x+y-1\right)$;<br/>$(4)\left(2x+3\right)\left(2x-3\right)-\left(2x-1\right)^{2}$.

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