
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
Among all the natural numbers from 1 to 20 inclusive, some 10 numbers are colored blue, and the remaining 10 are colored red. Then all possible sums of pairs of numbers, one of which is blue and the other is red, are calculated. What is the maximum number of different sums that can be among the hundred obtained numbers?

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