
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:
\[ \frac{2 + 5}{3^{105}} + \frac{2 + 2 \cdot 5}{3^{104}} + \frac{2 + 3 \cdot 5}{3^{103}} + \dots + \frac{2 + 104 \cdot 5}{3^2} + \frac{2 + 105 \cdot 5}{3}. \]

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