
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
What is the greatest number of subsequences of the form \( n, n+1, n+2 \) that a sequence of 2007 natural numbers can have? For example, the sequence \( 1,2,2,3,3 \) has 4 such subsequences.

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