
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
Let \( n > 4 \) be a positive integer. Determine the number of ways to walk from \( (0,0) \) to \( (n, 2) \) using only up and right unit steps such that the path does not meet the lines \( y = x \) or \( y = x - n + 2 \) except at the start and at the end.

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