
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
$$
\sum_{i=1}^{n-1} f(x_{i}) = f(x_{n}),
$$
then the maximum value of the positive integer \( n \) is...

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