
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 $16$ smaller squares. Each square is painted either red or blue randomly and independently with each color being equally likely. The square is rotated $90^\circ$ counterclockwise. After the rotation, any red square that has moved into a position that was occupied by a blue square is repainted blue. What is the probability that the entire grid is blue after this operation?
A) $\frac{1}{256}$
B) $\frac{1}{4096}$
C) $\frac{1}{65536}$
D) $\frac{1}{16384}$
E) $\frac{1}{1024}$

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