
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/>$(1)-{1^2}+\sqrt[3]{{64}}-(-2)×\sqrt{9}$;<br/>$(2)\sqrt[3]{-8}-\sqrt{2}+(\sqrt{3})^{2}+|1-\sqrt{2}|-\left(-1\right)^{2021}$.

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