
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
Teacher Li wrote an expression $(ax^{2}+bx+2)-(5x^{2}+3x)$, where $a$ and $b$ are constants representing coefficients. Then, the teacher asked students to assign different numerical values to $a$ and $b$ for calculation.<br/>$(1)$ Student A provided a set of data, and the final result of the calculation was $2x^{2}-4x+2$. Find the values of $a$ and $b$ provided by Student A, $a=$______, $b=$______; <br/>$(2)$ Student B provided a set of data $a=5$, $b=-3$. Simplify the expression based on the values provided by Student B; <br/>$(3)$ Student C provided a set of numbers, and the final result of the calculation is independent of the value of $x$. Find the values of $a$ and $b$ provided by Student C and calculate the final result of the expression.

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