
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
Given $A=x^{2}-2xy+y^{2}$, $B=x^{2}+2xy+y^{2}$, if $3A-2B+C=0$.<br/>$(1)$ What is the expression for the algebraic term $C$?<br/>$(2)$ If $x=\frac{1}{2}$, $y=-2$, what is the value of $C$?

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