
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 $n$ standard 12-sided dice are rolled, each showing a number from 1 to 12, the probability of obtaining a sum of 780 is greater than zero and is the same as the probability of obtaining a sum of $S$. The smallest possible value of $S$ is
**A) 60  B) 62  C) 65  D) 67  E) 70**

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