
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
Xiao Ming did a problem: "Given two polynomials $A$ and $B$, where $A=2x^{2}-5x+6$, calculate: $A-B$. He mistakenly wrote $A+B$ instead of $A-B$, and the result was $4x^{2}-4x+6$.  
$(1)$ Find the polynomial $B$;  
$(2)$ Find the correct result of $A-B$.

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