
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
Points \(A(0,0)\), \(B(n, 0)\), \(C(n, n)\), and \(D(0, n)\) determine a square. We color the lattice points on and inside this square either red or green such that each unit square within the larger square has exactly two red vertices. In how many ways can we accomplish this?

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