
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 a certain infinite geometric series with a common ratio is greater than the sum of the infinite geometric series $\frac{5}{12}, \frac{5}{16}, \ldots$ The first term of the given series is the same as the first term of the series mentioned. Calculate the common ratio and the sum of both geometric series.

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