
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
Arrange the quadratic polynomial in terms of the variable $x$ in descending order, and record it as $\left(a,b,c\right)$ according to the coefficients and constants. $\left(a,b,c\right)$ is called the characteristic numbers of the polynomial. For example, the characteristic numbers of the polynomial $-3x^{2}+4x-2$ are $\left(-3,4,-2\right)$, and the characteristic numbers of the polynomial $2x^{2}-1$ are $\left(2,0,-1\right)$. If the characteristic numbers of the difference between the polynomial $A$ and the polynomial $2x^{2}-4x-2$ are $\left(1,-4,6\right)$, then the polynomial $A$ is ______.

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