
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 has contracted the flu. After two rounds of infection, a total of 121 people have contracted the flu. On average, how many people does one person infect in each round of transmission? 

Solution: Let's assume that on average, one person infects x people in each round of transmission. 

(1) Express the number of people who have contracted the flu after the first round using an expression containing x: After the first round, a total of ①______ people have contracted the flu. In the second round of transmission, each of these people infects x people, resulting in a total of ②______ people contracting the flu after the second round. 

(2) Based on the given information, write the corresponding equation as ③______. 

(3) Solve this equation to obtain ④______. 

(4) Based on the practical meaning of the problem, on average, one person infects ⑤______ people.

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