
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
The health department conducted food hygiene inspections (referred to as inspections) on 4 student canteens at a university. If an inspection fails, rectification is required, and if it fails again after rectification, the canteen will be forcibly closed. Assume that the inspection outcomes of each canteen are independent of each other, and the probability of passing the inspection before rectification is 0.5, while the probability of passing after rectification is 0.8. Calculate (the results should be expressed as decimals, accurate to 0.01):  
(1) The probability that exactly one canteen needs rectification;  
(2) The probability that at least one canteen is closed.

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