
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 positive integers \( x_{1} < x_{2} < \cdots < x_{n} \) such that \( x_{1} + x_{2} + \cdots + x_{n} = 2003 \) and \( n \geqslant 2 \), find the minimum value of \( f(n) = n (x_{1} + x_{n}) \).

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