
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
(I) Find the value of $\int_{0}^{3}{\sqrt{9-{{x}^{2}}}}dx$;

(II) Given the function $f(x)=\begin{cases} {{x}^{2}}, & 0\leqslant x\leqslant 1 \\ \frac{1}{x}, & 1\leqslant x\leqslant e \end{cases}$ (where $e$ is the base of the natural logarithm), find the value of $\int_{0}^{e}{f(x)dx}$.

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