
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
Consider a colored $4 \times 4$ grid where each cell is filled with a unique color. Each cell of the grid is to be filled with either a 0 or a 1 such that the product of the numbers in any two adjacent cells is always 0. How many different ways are there to fill the grid?

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