
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
a) A person had a basement lit by three electric bulbs. The switches for these bulbs were located outside the basement, so to see which bulb was lit upon flipping any switch, the owner had to go down to the basement. One day, the person came up with a way to determine which switch controlled each bulb by going to the basement exactly once. What is this method?

b) How many bulbs and switches can be identified with each other if you are allowed to go down to the basement twice?

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