
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
Given the function \( f(x)=x+\frac{4}{x}-1 \), if there exist \( x_{1}, x_{2}, \cdots, x_{n} \in \left[ \frac{1}{4}, 4 \right] \) such that \( f(x_{1}) + f(x_{2}) + \cdots + f(x_{n-1}) = f(x_{n}) \), find the maximum value of the positive integer \( n \).

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