
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 $T_{n}$ represent the sum of the first $n$ terms of the arithmetic sequences ${a_{n}}$ and ${b_{n}}$, respectively. Given that $\frac{S_{n}}{T_{n}} = \frac{2n+1}{4n-2}$ for all positive integers $n$, find the value of $\frac{a_{10}}{b_{3}+b_{18}} + \frac{a_{11}}{b_{6}+b_{15}}$.

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