
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
Find 3 numbers, given that the product of the sum of the first two numbers with the third is 35, the product of the sum of the first and third numbers with the second is 27, and the product of the sum of the second and third numbers with the first is 32.

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