
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 is partitioned into $16$ unit squares. Each unit square is painted either white or black, with each color being equally likely, chosen independently at random. The square is then rotated $90^\circ$ clockwise around its center. Any white square in a position formerly occupied by a black square is repainted black. The colors of all other squares remain unchanged. What is the probability that the entire grid is completely black afterward?
A) $\frac{1}{4096}$
B) $\frac{1}{16384}$
C) $\frac{1}{32768}$
D) $\frac{1}{65536}$
E) $\frac{1}{131072}$

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