
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
Define a $\emph{brilliant integer}$ as an even integer that is greater than 20, less than 120, and such that the sum of its digits is 10. What fraction of all brilliant integers is divisible by 15? Express your answer as a common fraction.

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