
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 is a lamp on each cell of a $5 \times 5$ grid. When a lamp is turned on or off, its neighboring lamps connected by an edge also change their state. Initially, all the lamps are off. Martin comes and activates certain switches. In the end, only one lamp is on. What are the possible positions of this lamp?

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