
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 $0.abab\overline{ab}$ and $0.abcabc\overline{abc}$ satisfy
\[ 0.abab\overline{ab} + 0.abcabc\overline{abc} = \frac{17}{37}, \]
where $a$, $b$, and $c$ are (not necessarily distinct) digits. Find the three-digit number $abc$.

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