
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 flea is jumping on the vertices of square \(ABCD\), starting from vertex \(A\). With each jump, it moves to an adjacent vertex with a probability of \(\frac{1}{2}\). The flea stops when it reaches the last vertex it has not yet visited. Determine the probability that each vertex will be the last one visited.

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