
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
Let $0.\overline{ab}$ and $0.\overline{abcd}$ be two repeating decimals such that the sum satisfies:
\[ 0.\overline{ab} + 0.\overline{abcd} = \frac{27}{37}, \]
where $a$, $b$, $c$, and $d$ are the digits. Determine the four-digit number $abcd$.

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