
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
There are 111 lamps, each with its own switch. It is allowed to flip 13 of them at the same time. Initially, some lamps are on and some are off.

a) Is it possible to turn off all the lamps?

b) How many flips are required to do this if all the lamps were initially on?

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