
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 $S_n$ be the sum of the first $n$ terms of an arithmetic series with the first term $a$ and common difference $d$, and let $T_n$ be the sum of the first $n$ terms of another arithmetic series with the first term $b$ and common difference $2d$. The ratio $S_n : T_n$ varies according to the formula $\frac{S_n}{T_n} = \frac{9n + 3}{5n + 35}$. Determine the ratio of the fifteenth term of the first series to the fifteenth term of the second series.

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