
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 device consists of three independently operating elements. The probabilities of failure-free operation of the elements (over time $t$) are respectively: $p_{1}=0.7$, $p_{2}=0.8$, $p_{3}=0.9$. Find the probabilities that over time $t$, the following will occur:  
a) All elements operate without failure;  
b) Two elements operate without failure;  
c) One element operates without failure;  
d) None of the elements operate without failure.

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