
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
Petya tells his neighbor Vova: "There are 30 people in our class and an interesting situation is observed: any two boys have a different number of female friends in the class, and any two girls have a different number of male friends in the class. Can you determine how many boys and how many girls are in our class?" Vova replies: "You must be mistaken, such a situation cannot exist!" a) Is Vova right? b) How would you answer Petya's question?

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