
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
In a chess tournament for the master sportsman title, 12 players participated, with each player playing one game against every other player. A victory in a game is awarded 1 point, a draw 0.5 points, and a loss 0 points. To be awarded the title of master sportsman, a player needed to score more than 70% of the points achievable by winning all games. Could 

a) 7 participants;

b) 8 participants;

have been awarded the title of master sportsman?

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