
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

Group the set of positive odd numbers $\{1, 3, 5, \cdots\}$ in increasing order such that the $n$-th group has $(2n-1)$ odd numbers:
\[
\{1\}, \quad \{3, 5, 7\}, \quad \{9, 11, 13, 15, 17\}, \cdots
\]
(first group)(second group)(third group)

Determine which group 1991 belongs to.

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