
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
Given the set \( K(n, 0) = \varnothing \). For any non-negative integers \( m \) and \( n \), define \( K(n, m+1) = \{ k \mid 1 \leq k \leq n, K(k, m) \cap K(n-k, m) = \varnothing \} \). Find the number of elements in the set \( K(2004, 2004) \).

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