
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
Divide the sequence $\{2n+1\}$ into groups as follows: (3), (5, 7), (9, 11, 13), (15, 17, 19, 21), (23), (25, 27), (29, 31, 33), (35, 37, 39, 41), and so on. Find the sum of the numbers in the 100th group.

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