You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
In a chess tournament, each of the 10 players played one game against each other, and Petya took the last place (scored fewer points than any other participant). Then two players were disqualified, and all the points earned in the matches against them were canceled, and these two players were excluded from the table. As a result, Petya became the winner of the tournament (scored more points than any other participant). How many points could Petya score in the end (after the disqualification of the players)? A win gives 1 point, a draw gives 0.5 points, and a loss gives 0 points.
user
4
rule
In a chess tournament, each of the 10 players played one game against each other, and Petya took the last place (scored fewer points than any other participant). Then two players were disqualified, and all the points earned in the matches against them were canceled, and these two players were excluded from the table. As a result, Petya became the winner of the tournament (scored more points than any other participant). How many points could Petya score in the end (after the disqualification of the players)? A win gives 1 point, a draw gives 0.5 points, and a loss gives 0 points.
train