
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  $2n-1$  lamps in a row. In the beginning only the middle one is on (the  $n$ -th one), and the other ones are off. Allowed move is to take two non-adjacent lamps which are turned off such that all lamps between them are turned on and switch all of their states from on to off and vice versa. What is the maximal number of moves until the process terminates?

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