
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 an equilateral triangle ABC, a student starts from point A and moves the chess piece using a dice-rolling method, where the direction of the movement is determined by the dice roll. Each time the dice is rolled, the chess piece is moved from one vertex of the triangle to another vertex. If the number rolled on the dice is greater than 3, the movement is counterclockwise; if the number rolled is not greater than 3, the movement is clockwise. Let Pn(A), Pn(B), Pn(C) denote the probabilities of the chess piece being at points A, B, C after n dice rolls, respectively. Calculate the probability of the chess piece being at point A after 7 dice rolls.

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