
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
A square area of size $100 \times 100$ is tiled with $1 \times 1$ square tiles in four colors: white, red, black, and gray, such that no two tiles of the same color touch each other (i.e., do not share a side or a vertex). How many red tiles could there be?

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