
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 nonnegative integer values. Also, for all \( m, n \),

\[ f(m+n) - f(m) - f(n) = 0 \text{ or } 1 \]

with the conditions:

\[ f(2) = 0, \quad f(3) > 0, \quad \text{and} \quad f(9999) = 3333. \]

Determine \( f(1982) \).

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