
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
New definition: If $a+b=2$, then $a$ and $b$ are called balanced numbers about $2$.  
$(1)$ If $3$ and ______ are balanced numbers about $2$;  
$(2)$ ______ and $5-x$ are balanced numbers about $2$; (express using an algebraic expression with $x$)  
$(3)$ If $a=2x^{2}-3(x^{2}+x)+4$ and $b=2x-[3x-(4x+x^{2})-2]$, determine whether $a$ and $b$ are balanced numbers about $2$, and explain the reason.

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