
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
To solve the equation $(x^{2}-1)^{2}-5(x^{2}-1)+4=0$, we can treat $x^{2}-1$ as a whole, and then let $x^{2}-1=y$, so $(x^{2}-1)^{2}=y^{2}$, the original equation becomes $y^{2}-5y+4=0$.①  
Solving, we get $y_{1}=1$, $y_{2}=4$.  
When $y=1$, $x^{2}-1=1$, so $x^{2}=2$, and $x=\pm \sqrt{2}$;  
When $y=4$, $x^{2}-1=4$, so $x^{2}=5$, and $x=\pm \sqrt{5}$.  
Therefore, the solutions to the original equation are $x_{1}=\sqrt{2}$, $x_{2}=-\sqrt{2}$, $x_{3}=\sqrt{5}$, $x_{4}=-\sqrt{5}$.  
Answer to the question:  
$(1)$ Fill in the blanks: In the process of obtaining equation ① from the original equation, the use of substitution method achieved the purpose of reducing the degree, reflecting the mathematical idea of transformation.  
$(2)$ Solve the equation: $x^{4}-x^{2}-6=0$.

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