
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 solution process below and answer the questions. In the product of the polynomial $(x^{2}+ax+b)(2x^{2}-3x-1)$ with respect to $x$, the coefficient of the cubic term is $-5$, and the coefficient of the quadratic term is $-6$. Find the values of $a$ and $b$. Solution: $(x^{2}+ax+b)(2x^{2}-3x-1)$  
$=2x^{4}-3x^{3}+2ax^{3}+3ax^{2}+2bx^{2}-3bx\ldots \ldots $①  
$=2x4-\left(3-2a\right)x3-\left(3a-2b\right)x^{2}-3bx.\ldots \ldots $②  
According to the equality of corresponding coefficients, we have $\left\{\begin{array}{l}{3-2a=-5}\\{3a-2b=-6}\end{array}\right.\ldots \ldots $③  
Solving, we get $\left\{\begin{array}{l}{a=4}\\{b=9}\end{array}\right.\ldots \ldots $④  
$(1)$ Is the above solution process correct? ______;  
$(2)$ If incorrect, at which step did the error occur? ______;  
$(3)$ Write down the correct solution process.

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