
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
A right-angled triangle has sides of integer length. One of its sides has length 20. List all the different possible hypotenuses of such triangles and find the sum of all the numbers in this list.

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