
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
Several numbers form an arithmetic progression, and their sum is 63, with the first term being one and a half times the common difference. If each term of the progression is decreased by the same amount such that the first term of the progression equals the common difference, then the sum of all the numbers will decrease by no more than 8, but no less than 7. Determine the possible value of the common difference of this progression.

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