
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 chess piece starts from point $A$ in the diagram, and its movement is determined by the result of rolling a die. If the result is 1 or 2, the piece remains stationary; if the result is 3 or 4, the piece moves up one square; if the result is 5 or 6, the piece moves right one square.

(1) What is the probability that the piece reaches point $B$ within 8 steps (including 8 steps)?

(2) If it is stipulated that when the piece remains stationary for two consecutive turns, it moves right one square, what is the probability that the piece will pass through point $C$ if it continues to move indefinitely?

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