
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 x 4 square grid is partitioned into 16 unit squares, each randomly painted black or white with equal probability. The grid undergoes a 180° rotation about its center. After rotation, any white square that lands in a position previously occupied by a black square is repainted black, whereas all other squares keep their original colors. Calculate the probability that the entire grid is black after this process.

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