
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 the addition shown below where $A$, $B$, $C$, and $D$ are distinct digits, and there exists a carry into the last column, determine the number of different values possible for $D$. $\begin{tabular}{cccccc} & A & B & B & C & B \\+ & B & C & A & D & A \\ \hline & D & B & D & D & D \end{tabular} $

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