
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 the definition that an arithmetic sequence is a sequence in which the difference between any term and its preceding term is a constant. For example, the sequence $2, 4, 6, 8, \ldots$ is an arithmetic sequence. A second-order arithmetic sequence is defined as a sequence in which the differences between successive terms form a new sequence that is an arithmetic sequence itself. For instance, the sequence $1, 3, 7, 13, 21, \ldots$ is a second-order arithmetic sequence since the differences between successive terms form the sequence $2, 4, 6, 8, \ldots$, which is an arithmetic sequence.
1. Find the 100th term and the sum of the first 100 terms of the arithmetic sequence $2, 4, 6, 8, \ldots$.
2. Find the 6th term of the second-order arithmetic sequence $1, 3, 7, 13, 21, \ldots$.
3. Find the 2013th term of the second-order arithmetic sequence $1, 3, 7, 13, 21, \ldots$.

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