
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 are in arithmetic progression. If the smallest number is multiplied by 2, the largest number is increased by 7, and the middle number remains unchanged, the product of these new three numbers is 1000, and these three numbers form a geometric progression. Find the common difference of the arithmetic progression.

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