
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 series of numbers arranged according to a certain rule: $\sqrt{3}$, $\frac{{\sqrt{8}}}{2}$, $\frac{{\sqrt{15}}}{3}$, $\frac{{\sqrt{24}}}{4}$, $\ldots$ The $6$th number is ______, the $n$th number is ______.

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