
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
When $9$ fair standard $6$-sided dice are thrown, the probability that the sum of the numbers on the top faces is at least $18$, and at most two of these dice throw a maximal roll of $6$, can be written as \[\frac{m}{6^{9}},\] where $m$ is a positive integer. What is $m$?
A) 10626
B) 12870
C) 13662
D) 14400
E) 15015

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