
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/>$(1)\left(-1\right)^{3}+|2-\sqrt{5}|+(\frac{π}{2}-1.57)^0+\sqrt{20}$.<br/>$(2)(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})+(\sqrt{3}-1)^2$.<br/>$(3)\sqrt{16}-\sqrt[3]{-8}+\sqrt[3]{\frac{1}{27}}$;<br/>$(4)\sqrt{2}(\sqrt{2}+\frac{1}{\sqrt{2}})$.

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