
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 $R$. If $f(0) = 2008$ and for any $x \in R$, it satisfies $f(x+2) - f(x) \leq 3 \cdot 2^{x}$ and $f(x+6) - f(x) \geq 63 \cdot 2^{x}$, then $f(2008) =$ ____.

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