
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 geometric sequences have their first terms forming a geometric sequence with a common ratio of \( q_3 = 2 \). The common ratios of the three geometric sequences form an arithmetic sequence with a difference of \( d = 1 \). The sum of the second terms of the three geometric sequences is 24, and the sum of the first three terms of the third geometric sequence is 84. Write down these three geometric sequences.

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