
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
Lenka had a paper flower with eight petals. Each petal had a unique digit written on it, with no digit repeating on any petal. When Lenka played with the flower, she realized a few things:

- It was possible to detach four petals such that the sum of the numbers on these petals was equal to the sum of the numbers on the remaining petals.
- It was also possible to detach four petals such that the sum of the numbers on these petals was twice as large as the sum of the numbers on the remaining petals.
- It was even possible to detach four petals such that the sum of the numbers on these petals was four times as large as the sum of the numbers on the remaining petals.

Determine the digits that could have been written on the petals.

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