
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 $S_n:T_n=(5n+3):(3n+35)$ for all n, 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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