
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 $3 \times 3$ square is split into $9$ unit squares. Each unit square is initially either white or black, each color being equally likely, chosen independently and at random. The square undergoes two subsequent $90^\circ$ clockwise rotations about its center. After each rotation, any white square landing on a spot that was previously black is painted black. What is the probability that the grid is fully black after the two rotations?
A) $\frac{6561}{131072}$
B) $\frac{1}{2}$
C) $\frac{1}{4}$
D) $\frac{1}{65536}$
E) $\frac{1}{16}$

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