
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
Joãozinho wrote a multiplication problem on the board, and then Pedrinho replaced the digits with symbols and letters as shown below:

$$
\begin{array}{r}
\star \star \star \star \star \star \star A \\
\times \quad A \\
\hline B B B B B B B B B
\end{array}
$$

The letter $A$ represents the same digit regardless of its position, and the same rule applies to the letter $B$. The stars $\star$ can represent different digits from one another. What multiplication did Joãozinho write?

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