
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 Benoît's house, there are 2023 switches and \(2023 \times 1011\) light bulbs. Each bulb corresponds to a pair of switches and lights up precisely when both switches are turned on. However, Benoît forgot to label the bulbs, and he does not remember which pair of switches corresponds to which bulb. Initially, all switches are off. Each minute, Benoît can change the state of a single switch and then note the state of the bulbs. What is the minimum amount of time Benoît will need to determine all the correspondences between his bulbs and switches?

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