
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  $n$  be positive integers. Denote the graph of  $y=\sqrt{x}$  by  $C,$  and the line passing through two points  $(n,\ \sqrt{n})$  and  $(n+1,\ \sqrt{n+1})$  by  $l.$  Let  $V$  be the volume of the solid obtained by revolving the region bounded by  $C$  and  $l$  around the  $x$  axis.Find the positive numbers  $a,\ b$  such that  $\lim_{n\to\infty}n^{a}V=b.$ 

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