
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
Given a sequence of positive integers $\left\{a_{n}\right\}$ such that:
$$
\begin{array}{l}
a_{1}=a, a_{2}=b, \\
a_{n+2}=\frac{a_{n}+2018}{a_{n+1}+1} \quad (n \geqslant 1),
\end{array}
$$
find all possible values of $a + b$.

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