
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 sum of the terms of an infinite geometric series is 2 and the sum of the squares of the corresponding terms of this series is 6. Find the sum of the cubes of the corresponding terms.

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