
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 $(a_n)$ and $(b_n)$ be arithmetic sequences, and let $T_n$ and $S_n$ be the sums of the first $n$ terms of $(a_n)$ and $(b_n)$, respectively. Given that $\frac{S_n}{T_n} = \frac{n}{2n-1}$, find the value of $\frac{a_6}{b_6}$.

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