
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
In the exploration learning of the math group, Xiao Hua and his group members encountered the following question: Given $a=\frac{1}{2+\sqrt{3}}$, find the value of $2a^{2}-8a+1$. They solved it as follows: 

Since $\frac{1}{2+\sqrt{3}}=\frac{2-\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}=2-\sqrt{3}$, 

Therefore, $a-2=-\sqrt{3}$, 

Thus, $(a-2)^{2}=3$ which implies $a^{2}-4a+4=3$, 

Therefore, $a^{2}-4a=-1$, 

Hence, $2a^{2}-8a+1=2(a^{2}-4a)+1=2\times \left(-1\right)+1=-1$. 

According to Xiao Hua's group's solution method and process, please solve the following problems: 

(1) $\frac{1}{\sqrt{3}+\sqrt{2}}=\_\_\_\_\_\_$. 

(2) Simplify $\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+\frac{1}{\sqrt{4}+\sqrt{3}}+\ldots+\frac{1}{\sqrt{169+\sqrt{168}}}+\frac{1}{\sqrt{170}+\sqrt{169}}$. 

(3) If $a=\frac{1}{\sqrt{5}-2}$, then the value of $a^{4}-4a^{3}-4a+7$ is ______.

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