
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 Let \\(S_{n}\\) and \\(T_{n}\\) be the sums of the first \\(n\\) terms of the arithmetic sequences \\(\{a_{n}\}\\) and \\(\{b_{n}\}\\), respectively, and \\( \frac {S_{n}}{T_{n}}= \frac {n}{2n+1} (n∈N^{*})\\), determine the value of \\( \frac {a_{6}}{b_{6}}\\).

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