
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
Arrange all positive odd numbers in ascending order. Let the first number be \(a_{1}\), the sum of the next two numbers be \(a_{2}\), the sum of the next three numbers be \(a_{3}\), and so on. This forms the sequence \(\{a_{n}\}\), i.e., \(a_{1} = 1\), \(a_{2} = 3+5\), \(a_{3} = 7+9+11\), and so forth. Find the sum of the first 20 terms of the sequence \(a_{1} + a_{2} + \cdots + a_{20}\).

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