
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
Xiao Ming throws a die with uniform density three times and observes the number of points on the upper face each time. It is known that the numbers of points in the three throws are all different. Calculate the probability that the sum of the three numbers of points does not exceed $8$.

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