
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
Determine the exact value of the series
\[
\frac{1+1}{3 + 1} + \frac{2+1}{3^2 + 1} + \frac{4+1}{3^4 + 1} + \frac{8+1}{3^8 + 1} + \frac{16+1}{3^{16} + 1} + \dotsb.
\]

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