
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
The first term of the sequence $\{a_n\}$ is 1, and the remaining terms are either 1 or 2. Between the $k$th 1 and the $(k+1)$th 1, there are $2k-1$ number of 2s. The sequence $\{a_n\}$ is as follows: 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, …. Let $S_n$ denote the sum of the first $n$ terms of the sequence $\{a_n\}$. Find $S_{2019}$ (answer with a number).

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