
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
In a $2017 \times 2017$ grid, each cell contains a light, which can be either on or off. A light is termed "faulty" if and only if it has an even number of neighboring lights that are on. Find the minimum possible number of faulty lights in this $2017 \times 2017$ grid.

Note: Two lights are considered neighbors if their cells share a common edge.

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