
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 crawls on an $n \times n$ grid from the lower left node $A$ to the upper right node $B$, moving only right or up. What is the expected number of turns in the fly's trajectory if at each node, where there is a branching, 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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