
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 the sum of the first n terms of two arithmetic sequences, ${a_n}$ and ${b_n}$, are $S_n$ and $T_n$ respectively, and the ratio $\frac{S_n}{T_n} = \frac{2n+1}{3n+2}$, calculate the value of $\frac{a_3 + a_{11} + a_{19}}{b_7 + b_{15}}$.

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