
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
"Rock, Paper, Scissors" is an ancient game widely spread among the people in our country. The rules are: three different hand gestures represent rock, paper, and scissors respectively; two players show their gestures at the same time for 1 round of the game, "rock" beats "scissors", "scissors" beats "paper", and "paper" beats "rock". If both players show the same gesture, the game is a draw. Now, assume that when players A and B play the game, the chances of showing any of the three gestures are equally likely.

(1) List all possible outcomes of the gestures shown by players A and B in one game.

(2) Calculate the probability that player A does not lose to player B in one game.

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