
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
Given a $4 \times 4$ square partitioned into $16$ unit squares, each painted either white or black with equal likelihood, determine the probability that the grid is now entirely black after the described transformations.

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