
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
Let $S_n$ and $T_n$ be the respective sums of the first $n$ terms of two arithmetic series. If $\frac{S_n}{T_n} = \frac{9n+5}{6n+31}$ for all $n$, find the ratio of the fifteenth term of the first series to the fifteenth term of the second series.
A) \( \frac{11}{9} \)  
B) \( \frac{92}{71} \)  
C) \( \frac{78}{65} \)  
D) \( \frac{55}{43} \)

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