
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]


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Given two arithmetic sequences $\{a\_n\}$ and $\{b\_n\}$ with the sum of their first $n$ terms represented by $S_n$ and $T_n$ respectively. If for any natural number $n$, the ratio $\frac{S_n}{T_n} = \frac{2n-3}{4n-3}$ holds true, find the value of $\frac{a_3 + a_{15}}{2(b_3 + b_9)} + \frac{a_3}{b_2 + b_{10}}$.

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