
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
All natural numbers from 1 to 20 are divided into pairs, and the numbers in each pair are summed. What is the maximum number of the resulting ten sums that can be divisible by 11? Justify your answer.

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