
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
Alex paints cells inside a $6 \times 6$ square drawn on graph paper. Then he marks those nodes (intersections of the graph paper lines) that are adjacent to an equal number of painted and unpainted squares. What is the maximum number of nodes that can be marked?

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