
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
From $n^{2}$ light bulbs, a $n \times n$ scoreboard was assembled. Each light bulb has two states: on and off. When any light bulb is pressed, its state remains the same, but all the bulbs in the same row and column change their state to the opposite. Initially, all the bulbs on the scoreboard are off. Petya sequentially pressed several bulbs, resulting in the scoreboard not being completely turned off. What is the minimum number of bulbs that can be lit on the scoreboard?

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