
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
A twenty-sided die has 18 faces numbered from 1 through 17 and 19, and has two blank faces. Another similar die has 18 faces numbered from 1 to 15 and from 17 to 20, omitting number 16, and has two blank faces. When both of these dice are rolled, what is the probability that their sum equals 30? Express your answer as a common fraction.

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