
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 $\mathbf{R}$, such that for any $x \in \mathbf{R}$, we have $f(x+3) \leq f(x) + 3$ and $f(x+2) \geq f(x) + 2$. Let $g(x) = f(x) - x$. If $f(4) = 2008$, find $f(2008)$.

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