
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 $6 \times 6$ toy board, each cell represents a light button. When someone presses a button, it lights up if it is off and turns off if it is on. Additionally, all buttons that share a side with the pressed button also change their state: from on to off or from off to on. Starting with all buttons off and pressing each button on the board exactly once, one at a time and in any order, how many buttons will be lit at the end?

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