
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
There are 101 numbers written in a sequence (the numbers are not necessarily integers). The arithmetic mean of all the numbers except the first one is 2022, the arithmetic mean of all the numbers except the last one is 2023, and the arithmetic mean of the first and last numbers is 51. What is the sum of all the written numbers?

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