
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
Consider a fair $8$-sided die with sides numbered from $1$ to $8$. This die is rolled repeatedly until a number greater than $6$ appears. Find the probability that each of the odd numbers $1$, $3$, and $5$ appears at least once before the first occurrence of a number greater than $6$.

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