
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 that \( S_n \) and \( T_n \) are the sums of the first \( n \) terms of the arithmetic sequences \( \{a_n\} \) and \( \{b_n\} \), respectively, and that
\[
\frac{S_n}{T_n} = \frac{2n + 1}{4n - 2} \quad (n = 1, 2, \ldots),
\]
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