
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
Let \( f \) be a function from the set of non-negative integers to itself, satisfying for all \( n \geqslant 0 \):
(1) \( [f(2n+1)]^2 - [f(2n)]^2 = 6 f(n) + 1 \);
(2) \( f(2n) \geqslant f(n) \).
How many numbers less than 2008 are in the range of \( f \)?

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