
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 on the positive integers and takes non-negative integer values.  $f(2)=0,f(3)>0,f(9999)=3333$  and for all  $m,n:$  \[ f(m+n)-f(m)-f(n)=0 \text{ or } 1. \] Determine  $f(1982)$ .

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