
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
Find distinct digits to replace the letters \(A, B, C, D\) such that the following division in the decimal system holds:

$$
\frac{ABC}{BBBB} = 0,\overline{BCDB \, BCDB \, \ldots}
$$

(in other words, the quotient should be a repeating decimal).

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