
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
Adva is given an arithmetic sequence with 8 terms and a geometric sequence with 4 terms. Each sequence's first term is 1, and their last terms are equal. The sum of the geometric sequence is 21 more than the last term of the arithmetic sequence. Determine the two sequences.

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