
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
Define a function \( f(x) \) on \(\mathbf{R}\), satisfying:

\[
\begin{cases}
f(x+2016) \leqslant f(x) + 2016, \\
f(x+2017) \geqslant f(x) + 2017,
\end{cases}
\]

and \( f(1) = 2 \). Let \( a_n = f(n) \) for \( n \in \mathbf{N}^* \). Then find \( a_{2018} \).

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