
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 $P_n$ and $Q_n$ be the respective sums of the first $n$ terms of two arithmetic series. If $P_n:Q_n=\frac{5n+3}{3n+11}$ for all $n$, find the ratio of the fifteenth term of the first series to the fifteenth term of the second series.
A) 3:5
B) 16:11
C) 71:52
D) 78:71

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