
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 two arithmetic sequences $\{a_n\}$ and $\{b_n\}$, the sums of the first $n$ terms are denoted as $S_n$ and $T_n$, respectively. If for any natural number $n$, it holds that $\dfrac{S_n}{T_n} = \dfrac{2n-3}{4n-3}$, calculate $\dfrac{a_3+a_{15}}{2(b_3+b_9)} + \dfrac{a_3}{b_2+b_{10}}$.

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