
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 solve the problem:<br/>Solve the equation $x^{4}-5x^{2}+4=0$. This is a fourth-degree equation. Based on the characteristics of this equation, the solution method is usually as follows:<br/>Let $x^{2}=y$, then $x^{4}=y^{2}$, so the original equation can be transformed into $y^{2}-5y+4=0$. Solving this equation gives $y_{1}=1$, $y_{2}=4$.<br/>When $y=1$, $x^{2}=1$, so $x=\pm 1$;<br/>When $y=4$, $x^{2}=4$, so $x=\pm 2$;<br/>Therefore, the original equation has four roots: $x_{1}=1$, $x_{2}=-1$, $x_{3}=2$, $x_{4}=-2$. Please refer to the example and solve the equation $(x^{2}+x)^{2}-4(x^{2}+x)-12=0$.

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