$2\mathrm{.}2[2$ points$]$ In which state is the DFA after consuming the following sequence of characters?

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Possible states are $0$ to $8,$ inclusive. Only $1$ state is the answer.

$2\mathrm{.}3[3$ points$]$ Consider a new scenario. Suppose you have the below, partially$-$completed Knuth$-$Morris$-$Pratt DFA for a string $\backslash ($ s $\backslash )$ of length $12$ over the alphabet $\backslash (\backslash \{\backslash$mathrm$\{$A$\},\backslash$mathrm$\{$B$\},\backslash$mathrm$\{$C$\}\backslash \}\backslash ).$ Reconstruct the string $\backslash ($ s $\backslash )$ in the space below. You do not need to complete the first three rows of the table, but completion of them may be used to allocate partial credit. Explain the thought process behind how you reconstructed string $\backslash ($ s $\backslash ).$