
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
\[0.abab\overline{ab}+0.abcabc\overline{abc}=\frac{33}{37},\]
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}
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