
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
A $5 \times 5$ square contains a light bulb in each of its cells. Initially, only one light bulb is on. You can change the state of the light bulbs in any $k \times k$ square, with $k > 1$. What are the initial positions of the light bulb that is on that allow turning off all the light bulbs?

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