
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 fly is crawling on an $n \times n$ grid from the bottom-left corner $A$ to the top-right corner $B$, moving only right or upward. What is the expected number of turns on the fly's path, given that at each branching node, the fly chooses the next segment of the path with equal probabilities?

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