
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
Consider a geometric sequence where the sum of the first 1500 terms is 300, and the sum of the first 3000 terms is 570. Determine the sum of the first 4500 terms of this sequence.

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