
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
The function \( f: \mathbf{N}^{\star} \rightarrow \mathbf{R} \) satisfies \( f(1)=1003 \), and for any positive integer \( n \), it holds that
\[ f(1) + f(2) + \cdots + f(n) = n^2 f(n). \]

Find the value of \( f(2006) \).

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