
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
Alyosha is shading cells within a $6 \times 6$ square drawn on graph paper. Then he marks the grid nodes (intersections of the graph paper lines) that are adjacent to an equal number of shaded and unshaded squares. What is the maximum number of nodes that can be marked?

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