
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
The repeating decimals $0.bcbc\overline{bc}$ and $0.bcabc\overline{bcabc}$ satisfy
\[0.bcbc\overline{bc} + 0.bcabc\overline{bcabc} = \frac{41}{111},\]
where $b$, $c$, and $a$ are (not necessarily distinct) digits. Find the three-digit number $bca$.

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