
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
In an arithmetic sequence, the product of the 2nd and 8th terms is 64, and the product of the 4th and 5th terms is 80. Determine the first 8 terms of this sequence (or sequences). Additionally, insert 4 new terms between the 7th and 8th terms of one of these sequences such that these terms form an arithmetic sequence with the 7th and 8th terms.

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