
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 sequence \\(\{a_n\}\) consists of numbers \\(1\\) or \\(2\\), with the first term being \\(1\\). Between the \\(k\\)-th \\(1\\) and the \\(k+1\\)-th \\(1\\), there are \\(2k-1\\) \\(2\\)s, i.e., the sequence \\(\{a_n\}\) is \\(1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, \ldots\\). Let the sum of the first \\(n\\) terms of the sequence \\(\{a_n\}\) be \\(S_n\\), then \\(S_{20} =\\)           , \\(S_{2017} =\\)                .

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