
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
Given the 10 numbers: \(10, 20, 30, \ldots, 100\). With these numbers, you can perform the following operation: select any three numbers and add one to each of the selected numbers. The same operation can then be performed on the resulting 10 numbers, and so on. Is it possible, after a number of operations, to obtain: a) all identical numbers? b) all numbers equal to 200?

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