
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
If the whole numbers from 1 to 10 are arranged into 5 pairs, with the sums of each pair being 11, 4, 7, 16, and 17, then can the numbers in each pair be uniquely determined? How many ways can the ten numbers be grouped into five pairs such that the sum of each pair is 9, 10, 11, 12, 13?

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