
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
Read the following material and answer the questions: Solve the equation $x^{4}-5x^{2}+4=0$. This is a fourth-degree equation in one variable. Based on the characteristics of this equation, the usual method to solve it is: Let $x^{2}=y$, then $x^{4}=y^{2}$, so the original equation can be transformed into $y^{2}-5y+4=0$ (1). Solving this, we get $y_{1}=1$ and $y_{2}=4$. When $y=1$, $x^{2}=1$, so $x=\pm 1$; when $y=4$, $x^{2}=4$, so $x=\pm 2$. Therefore, the original equation has four roots: $x_{1}=1$, $x_{2}=-1$, $x_{3}=2$, $x_{4}=-2$.

$(1)$ In the process of transforming the original equation into equation (1), using the method of substitution to reduce the degree reflects the transformation idea in mathematics.

$(2)$ Try to solve the equation $(x^{2}+x)^{2}-4(x^{2}+x)-12=0$ using the above method.

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