
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
A sequence of numbers: $\frac{1}{3}$, $\frac{2}{6}$, $\frac{3}{11}$, $\frac{4}{18}$, $\frac{5}{27}$, $\frac{6}{38}$, ..., they are arranged according to a certain rule, then the $n$th number $(n$ is a positive integer) is ______.

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