
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
Harper defines a $\emph{smart integer}$ as an odd integer that is greater than 30, less than 130, and such that the sum of its digits is 10. What fraction of all smart integers is divisible by 11? Express your answer as a common fraction.

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