
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 \( f(x) \) be a function defined on \( \mathbf{R} \). Given that \( f(0)=2008 \), and for any \( x \in \mathbf{R} \), it satisfies \( f(x+2)-f(x) \leq 3 \cdot 2^{x} \) and \( f(x+6)-f(x) \geq 63 \cdot 2^{x} \), find \( f(2008) \).

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