
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. Define the sequence $\left\{a_{n}\right\}$ where:

- $a_{1}$ is the first odd number,
- $a_{2}$ is the sum of the next two odd numbers,
- $a_{3}$ is the sum of the next three odd numbers, and so on.

For example:
$$
a_{1}=1, a_{2}=3+5, a_{3}=7+9+11, \cdots 
$$

Find the value of the sum $a_{1}+a_{2}+\cdots+a_{20}=$ $\qquad$

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