
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
Given that the sum of the first 20 terms of a geometric sequence is 21, and the sum of the first 30 terms is 49, find the sum of the first 10 terms of this geometric sequence.

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