
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
A and B are playing a dice game with two dice. The rules are as follows: If the sum of the points on the dice is a multiple of 3, the person who rolled the dice continues to roll; if the sum is not a multiple of 3, the other person takes their turn to roll. A starts the game by rolling first. If the probability that A rolls on the nth turn is \( P_{n} \), then \( P_{n} = \) ________

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