
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 first term of an arithmetic and geometric sequence is 5. The second term of the arithmetic sequence is 2 less than the second term of the geometric sequence. The third term of the geometric sequence is equal to the sixth term of the arithmetic sequence. The question is, which sequences satisfy these given conditions?

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