
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 \( f(n) \) is defined for all positive integers \( n \) and takes on non-negative integer values such that \( f(2)=0 \), \( f(3)>0 \), and \( f(9999)=3333 \). Also, for all \( m, n \):
$$
f(m+n)-f(m)-f(n)=0 \quad \text{or} \quad 1.
$$

Determine \( f(2005) \).

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