
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
We toss a die 30 times. Determine, with an accuracy of 8 decimal places, the probability that there will be at least one six among the numbers rolled, and that no five or four appears before the first six.

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