
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 fair $6$-sided die is repeatedly rolled until the number 4 appears. What is the probability that both other even numbers (2 and 6) and at least one odd number appear at least once before the first occurrence of 4?

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