
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 point moves along the edges of a cube \( ABCDA'B'C'D' \). From any vertex, it can move randomly along one of the three edges originating from that vertex, each with an equal probability of \( \frac{1}{3} \). The vertices \( B' \) and \( C' \) are special such that once the point reaches any of them, it stops moving. If the point starts from vertex \( A \), what is the probability that it:
1. Stops at vertex \( B' \)?
2. Stops at vertex \( C' \)?
3. Never reaches either vertex \( B' \) or vertex \( C' \)?

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