
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 $0.cdcd\overline{cd}$ and $0.cdecde\overline{cde}$ satisfy
\[0.cdcd\overline{cd} + 0.cdecde\overline{cde} = \frac{44}{99},\]
where $c$, $d$, and $e$ are (not necessarily distinct) digits. Find the three-digit number $cde$.

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