
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
There are three numbers in arithmetic progression. The triple of the sum of the first two numbers is exactly twice the third number. If the second number is reduced by 2, then the resulting number is the geometric mean of the first and third numbers. Find the original three numbers.

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