
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
In the "Black White Pair" game, a common game among children often used to determine who goes first, participants (three or more) reveal their hands simultaneously, using the palm (white) or the back of the hand (black) to decide the winner. If one person shows a gesture different from everyone else's, that person wins; in all other cases, there is no winner. Now, A, B, and C are playing the "Black White Pair" game together. Assuming A, B, and C each randomly show "palm (white)" or "back of the hand (black)" with equal probability, the probability of A winning in one round of the game is _______.

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