
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

Rewrite the original system of equations as

$$
\left\{\begin{array}{l}
a=-3 x^{2}+5 x-2 \\
(x+2) a=4\left(x^{2}-1\right)
\end{array}\right.
$$

Notice that $x=-2$ is not a solution to the second equation of the system. Hence, the system can be rewritten as

$$
\left\{\begin{array}{l}
a=-3 x^{2}+5 x-2 \\
a=\frac{4\left(x^{2}-1\right)}{x+2}
\end{array}\right.
$$

If the system is consistent, its solution satisfies the equation

$$
\frac{4\left(x^{2}-1\right)}{x+2}=-3 x^{2}+5 x-2
$$

Solve this equation by factoring the left and right sides:

$$
\frac{4(x-1)(x+1)}{x+2}=(x-1)(-3 x+2)
$$

The last equation reduces to

$$
x(x-1)(3 x+8)=0
$$

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