<|system|>
The sum of the two $5$-digit numbers $AMC10$ and $AMC12$ is $123422.$ What is $A + M + C?$</s>.
<|user|>
Can you answer based on context?
<|assistant|>
Since the last two digits of $AMC10$ and $AMC12$ sum to $22,$ we have \[
AMC + AMC = 2(AMC) = 1234.
\] Hence $AMC=617,$ so $A=6,$ $M=1,$ $C=7,$ and $A+M+C = 6+1+7 = 14.$