
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
The digits of a three-digit number form a geometric progression with distinct terms. If this number is decreased by 200, the resulting three-digit number has digits that form an arithmetic progression. Find the original three-digit number.

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