
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 $0.xyxy\overline{xy}$ and $0.xyzxyz\overline{xyz}$ satisfy
\[0.xyxy\overline{xy}+0.xyzxyz\overline{xyz}=\frac{39}{41},\]
where $x$, $y$, and $z$ are (not necessarily distinct) digits. Find the three digit number $xyz$.

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