
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 odd numbers from 1 to 2011 in order and group them according to the pattern of 1, 2, 3, 2, 1, 2, 3, 2, 1,... numbers per group, as in the following example (each group is enclosed in parentheses):
(1) $(3,5)(7,9,11)(13,15)(17)(19,21)(23,25,27)(29,31)(33) \ldots.$ Find the sum of the numbers in the last group.

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