
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
Define  $K(n,0)=\varnothing $  and, for all nonnegative integers m and n,  $K(n,m+1)=\left\{ \left. k \right|\text{ }1\le k\le n\text{ and }K(k,m)\cap K(n-k,m)=\varnothing  \right\}$ .  Find the number of elements of  $K(2004,2004)$ .

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