
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 you turn a lamp on or off, its neighboring lamps (adjacent by a side) also change their state. Initially, all the lamps are off. Martin arrives and activates certain switches. In the end, only one lamp is on. What are its possible positions?

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