
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
The pages of a notebook are consecutively numbered such that the first sheet has the numbers 1 and 2, the second sheet has the numbers 3 and 4, and so on. A sheet is torn out of this notebook. The sum of all the page numbers of the remaining sheets is calculated and the result is 2021.

(a) How many pages did the notebook originally have?

(b) What page numbers could be on the torn-out sheet?


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