
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
Evaluate the sum:
$$\frac{3^1}{5^1 - 2} + \frac{3^2}{5^2 - 2} + \frac{3^4}{5^4 - 2} + \frac{3^8}{5^8 - 2} + \cdots.$$

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