
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
Three numbers form a geometric progression. If the second number is increased by 2, the progression becomes arithmetic, and if the last number is then increased by 9, the progression becomes geometric again. Find these numbers.

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