
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
Suppose the repeating decimals $0.abcdabcd\overline{abcd}$ and $0.abcdefabcdef\overline{abcdef}$ satisfy:
\[0.abcdabcd\overline{abcd} + 0.abcdefabcdef\overline{abcdef} = \frac{49}{999},\]
where $a$, $b$, $c$, $d$, $e$, and $f$ are (not necessarily distinct) digits. Find the six-digit number $abcdef$.

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