
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
Lucas defined a $\emph{smart integer}$ as an even integer that is greater than 40, less than 150, and such that the sum of its digits is 10. What fraction of all smart integers is divisible by 10? Express your answer as a common fraction.

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