
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
Simplify or calculate:<br/>$(1){(-1)^{2021}}+\sqrt{8}-4sin45°+|-2|+{({\frac{1}{2}})^{-2}}$;<br/>$(2)\frac{{{x^2}-9}}{{{x^2}+2x+1}}÷({x+\frac{{3-{x^2}}}{{x+1}}})$.

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