
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 $4 \times 4$ grid is divided into $16$ unit squares. Each square is independently painted either white or black, with each color equally likely. The grid is then rotated $180\,^{\circ}$ about its center. After the rotation, any white square that does not land on a white square is painted black. Find the probability that the grid is completely black after this process.

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