
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 \( f(0) = 1008 \) and for any \( x \in \mathbf{R} \), the following conditions hold:
\[
\begin{array}{l}
f(x+4)-f(x) \leqslant 2(x+1), \\
f(x+12)-f(x) \geqslant 6(x+5) .
\end{array}
\]

Find the value of \( \frac{f(2016)}{2016} \).

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