
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 terms of three geometric sequences form a geometric sequence with a ratio of 2, and the ratios of these three geometric sequences form an arithmetic sequence with a difference of 1. The sum of the second terms of the three geometric sequences is 24, and the sum of the first terms of these three sequences is 84. Determine the three geometric sequences.

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