
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 function \( f(x_{1}, x_{2}, \ldots, x_{n}) \) is linear in each of the \( x_{i} \) and \( f(x_{1}, x_{2}, \ldots, x_{n}) = \frac{1}{x_{1} x_{2} \cdots x_{n}} \) when \( x_{i} \in \{3, 4\} \) for all \( i \). In terms of \( n \), what is \( f(5, 5, \ldots, 5) \)?

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