
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
Comprehensive application  
Please read the process of solving the equation $x^{4}=2x^{2}-3=0$.  
Solution: Let $x^{2}=y$, then the original equation can be transformed into $y^{2}-2y=3=0$,  
From $\left(y-1\right)^{2}=4$, we get $y_{1}=3$, $y_{2}=-1$,  
When $y=3$, $x^{2}=3$, $x_1=\sqrt{3}$, $x_2=-\sqrt{3}$,  
When $y=-1$, $x^{2}=-1$, no solution.  
Therefore, the solution to the original equation is $x_1=\sqrt{3}$, $x_2=-\sqrt{3}$.  
This method of solving equations is called substitution method.  
Use the above method to solve the following two equations:  
$(1)x^{4}-x^{2}-6=0$;  
$(2)(x^{2}+2x)^{2}-2(x^{2}+2x)-3=0$.

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