
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
Three fair dice, each with 8 sides, are rolled. What is the probability that the first die's number is strictly greater than the numbers on the second and third dice?
- **A)** \(\frac{35}{128}\)
- **B)** \(\frac{49}{512}\)
- **C)** \(\frac{70}{256}\)
- **D)** \(\frac{177}{512}\)

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