
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 plane Cartesian coordinate system, consider the set of points \(\{(m, n) \mid m, n \in \mathbf{N}, 1 \leqslant m, n \leqslant 6\}\), where each point is colored either red or blue. What is the number of different ways to color these points such that each unit square has exactly two red vertices?

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