
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
Danka had a paper flower with ten petals. Each petal had a unique digit written on it, with no digit repeating on any other petal. Danka tore off two petals such that the sum of the numbers on the remaining petals was a multiple of nine. Then, she tore off another two petals such that the sum of the numbers on the remaining petals was a multiple of eight. Finally, she tore off another two petals such that the sum of the numbers on the remaining petals was a multiple of ten.

Find the three sums that could sequentially remain after tearing off petals. Determine all such triplets of sums.

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