
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 arithmetic sequences $\{a_n\}$ and $\{b_n\}$, the sum of the first $n$ terms are $S_n$ and $T_n$ respectively. If $$\frac{S_n}{T_n} = \frac{2n}{3n+1}$$, then evaluate $\frac{a_4 + a_6}{b_3 + b_7}$.

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