
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 filled with white or black squares, each color equally likely, chosen independently at random, determine the probability that the grid is entirely black after rotation and color change.

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