
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 \( f(0)=1008 \), and for any \( x \in \mathbf{R} \), it holds that:
\[ f(x+4) - f(x) \leq 2(x+1) \]
\[ f(x+12) - f(x) \geq 6(x+5) \]
Find \( \frac{f(2016)}{2016} \).

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