
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, 29 participants are playing. A win in a match is awarded one point, a draw is awarded half a point, and a loss is zero points. If a player has no opponent, they receive 1 point, but according to the rules, a point without a game can be awarded to a player no more than once throughout the tournament. In the next round, participants with the same number of points play against each other (if this is not possible, opponents are chosen randomly). A total of 9 rounds were played. No draws were recorded in any round.

(a) Could two players with 8 points each play in the final round?

(b) Starting from which round, regardless of the results of the previous rounds, could no pair of players who had won all previous rounds meet?

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