
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 5 fair standard 6-sided dice are thrown, find the value of $n$ for the probability that the sum of the numbers on the top faces is $15$, given that the probability can be written as $\frac{n}{6^{5}}$.

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