
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
A person contracted the flu, and after two rounds of infection, a total of 64 people have contracted the flu.  
$(1)$ Find out how many people, on average, each person infected during each round of infection.  
$(2)$ If not controlled in time, how many people will be infected in the third round?

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