
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 grid partitioned into $16$ unit squares, each of which is painted white or black with a probability of $\frac{1}{2}$, determine the probability that the grid is entirely black after a $90^{\circ}$ clockwise rotation and any white square landing in a position previously occupied by a black square is repainted black.

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