
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
\[
\frac{3 + 12}{9^{100}} + \frac{3 + 2 \cdot 12}{9^{99}} + \frac{3 + 3 \cdot 12}{9^{98}} + \dots + \frac{3 + 98 \cdot 12}{9^3} + \frac{3 + 99 \cdot 12}{9^2} + \frac{3 + 100 \cdot 12}{9}.
\]

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