
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 $x_1, x_2, ..., x_n \in [\frac{1}{4}, 4]$ such that $f(x_1) + f(x_2) + ... + f(x_{n-1}) = f(x_n)$, then the maximum value of the positive integer $n$ is $\_\_\_\_\_\_$.

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