
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
After chickens are vaccinated with a certain vaccine, $80\%$ of them will not be infected with a certain virus. If $5$ chickens are vaccinated, find:<br/>$(1)$ the probability that no chicken is infected with the virus;<br/>$(2)$ the probability that exactly $1$ chicken is infected with the virus.

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