
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

After watching a movie, viewers rated the film one by one with an integer score from 0 to 10. At any given moment, the movie’s rating was calculated as the sum of all scores given, divided by their count. At a particular moment $T$, the rating turned out to be an integer, and then with each new voting viewer, it decreased by one unit. What is the maximum number of viewers who could have voted after moment $T$?

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