
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 $3 \times 3$ square that is partitioned into $9$ unit squares, each with equal likelihood of being painted white or black, calculate the probability that the entire grid is now entirely black after the given rotation and coloring.

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