
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
In a certain region, there are 5 factories. Due to a shortage of electricity, it is mandated that each factory must choose a day of the week to shut down (the choice of which day is equally likely). Assuming the choices among factories are independent of each other:  
(1) Calculate the probability that all 5 factories choose Sunday to shut down.  
(2) Calculate the probability that at least two factories choose the same day to shut down.

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