
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:<br/>$(1)(-1{)^{2018}}-(3-π{)^0}+(-\frac{1}{3}{)^{-2}}$;<br/>$(2)\left(x+1\right)\left(x+3\right)-\left(x-2\right)^{2}$;<br/>$(3)199^{2}-199\times 201(Use multiplication formula for convenience)$;<br/>$(4)(1-\frac{1}{{{2^2}}})(1-\frac{1}{{{3^2}}})(1-\frac{1}{{{4^2}}})⋯(1-\frac{1}{{{{2022}^2}}})(1-\frac{1}{{{{2023}^2}}})$.

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