
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
Several positive integers are given, not necessarily all different. Their sum is 2003. Suppose that \( n_1 \) of the given numbers are equal to 1, \( n_2 \) of them are equal to 2, ..., \( n_{2003} \) of them are equal to 2003. Find the largest possible value of

\[ n_2 + 2 n_3 + 3 n_4 + \cdots + 2002 n_{2003}. \]

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