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

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