
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
On the blackboard is written a sequence of numbers \(1, 2, 3, \cdots, 2011\). Each time, the first 16 numbers are erased, and the sum of these 16 numbers is written at the end of the sequence. This process continues until only one number is left. Determine:
(1) What is the final remaining number?
(2) What is the total sum of all the numbers that have ever appeared on the blackboard?

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