
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 an infinite geometric sequence \{a\_n}(n∈N*) with the first term a\_1=1 and common ratio q=13\*, find the limit of the sum of the first n terms S\_n, i.e., limn→∞Sn=\_\_\_\_\_\_.

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