
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
1. Compute $-3\frac{3}{8}^{-\frac{2}{3}}+(0.002)^{-\frac{1}{2}}-9(\sqrt{5}-2)^{-1}+3\pi^{0}-\sqrt{(1-\sqrt{5})^{2}}$
2. Compute $\sqrt[4]{8\times \sqrt{4}}+2\sqrt{3}\times \sqrt[3]{\frac{3}{2}}\times \sqrt[6]{12}+\sqrt[4]{(-2)^{2}}$
3. Given $x=\frac{a^{\frac{1}{n}}-a^{-\frac{1}{n}}}{2}$, where $n\in \mathbb{N}^{*}$, $a>0$ and $a\neq 1$, find the value of $(x-\sqrt{1+x^{2}})$.

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