
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 the limit of the ratio of an infinite decreasing geometric series \(\{a_{n}\}\) satisfies \(\lim _{n \rightarrow \infty} \frac{a_{1} + a_{4} + a_{7} + \cdots + a_{3n-2}}{a_{1} + a_{2} + \cdots + a_{n}} = \frac{3}{4}\), find the common ratio of the series.

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