
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
Given an arithmetic sequence $\{a_{n}\}$ and $\{b_{n}\}$ with the sums of the first $n$ terms being $S_{n}$ and $T_{n}$, respectively, if $\frac{S_n}{T_n}=\frac{3n+4}{n+2}$, find $\frac{a_3+a_7+a_8}{b_2+b_{10}}$.

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