
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 that A, B, C, and D are different digits, and the multiplication problem is represented as:
\[
\begin{array}{cccc}
& A & B & 1 \\
\times & & C & D \\
\hline
C & D & C & D \\
\end{array}
\]
where C ≠ 0 and D ≠ 0, calculate the value of A + B.

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