
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 $4 \times 4$ square grid is partitioned into $16$ unit squares. Each unit square is painted either white or black, each color being equally likely, chosen independently and at random. The square grid is then rotated twice (180 degrees in total) about its center. After each rotation, any white square that lands in a position that was originally black is repainted black. What is the probability that the grid is entirely black after the two rotations?
**A)** $\frac{1}{16384}$ 
**B)** $\frac{1}{65536}$
**C)** $\frac{1}{4096}$
**D)** $\frac{1}{1024}$

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