
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
To understand the integrity of students during exams, the school's political and educational office conducted the following random survey. Two questions were asked to the respondents:
(1) Is your student ID an odd number?
(2) Have you cheated during exams?

Respondents were required to toss a coin with their back to the surveyor. If it landed on heads, they would answer the first question; otherwise, they would answer the second question. The respondents did not need to tell the surveyor which question they were answering, only responding with "yes" or "no". Since only the respondents themselves knew which question they were answering, all answers were truthful. Among the 2000 surveyed students (with student IDs ranging from 1 to 2000), 510 people answered "yes". Calculate the number of students among these 2000 who have cheated based on probability knowledge.

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