
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 the sequence $\{2n+1\} (n\in\mathbb{N}^{*})$ sequentially in brackets with one number in the first bracket, two numbers in the second bracket, three numbers in the third bracket, four numbers in the fourth bracket, one number in the fifth bracket, and so on in a cycle, then calculate the sum of the numbers in the $120$th bracket.

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