
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  $f$  be a continuously differentiable function on  $[0, 1]$  and  $m \in \mathbb{N}$ . Let  $A = f(1)$  and let  $B=\int \limits_{0}^1 x^{-\frac{1}{m}}f(x)dx$ . Calculate   $$ \lim \limits_{n \to \infty} n\left(\int \limits_{0}^1 f(x)dx-\sum \limits_{k=1}^n \left(\frac{k^m}{n^m}-\frac{(k-1)^m}{n^m}\right)f\left(\frac{(k-1)^m}{n^m}\right)\right) $$  in terms of  $A$  and  $B$ .

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