
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
Compute the sum of the series:
\[
\frac{2 + 9}{8^{100}} + \frac{2 + 2 \cdot 9}{8^{99}} + \frac{2 + 3 \cdot 9}{8^{98}} + \dots + \frac{2 + 98 \cdot 9}{8^3} + \frac{2 + 99 \cdot 9}{8^2} + \frac{2 + 100 \cdot 9}{8}.
\]

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