
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
Five integers are written on the board. By adding them in pairs, the following set of 10 numbers was obtained: \(3, 8, 9, 16, 17, 17, 18, 22, 23, 31\). Determine the numbers written on the board. In the answer, write their product.

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