
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
Teams participating in a quiz need to answer 50 questions. The score (in integer points) for each correct answer is determined by the experts after the quiz, and the score for an incorrect answer is 0 points. The team's final score is the sum of the points earned from correct answers. It was found that the values assigned to correct answers could be altered such that the teams could be ranked according to any preference of the experts. What is the maximum number of teams that could have participated in the quiz?

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