
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
Three people, A, B, and C, are playing a game of "Black and White": In each round, A, B, and C randomly show either the "palm (white)" or the "back of the hand (black)" gesture. If one person's gesture is different from the other two, that person wins; otherwise, there is no winner. The probability that person A wins in one round is ___.

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