
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
Machines A, B, and C operate independently and are supervised by a single worker, who cannot attend to two or more machines simultaneously. Given that the probabilities of these machines operating without needing supervision are 0.9, 0.8, and 0.85 respectively, calculate the probability that during a certain period,  
(1) all three machines operate without needing supervision;  
(2) the worker is unable to supervise effectively, leading to a shutdown.

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