
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
Evaluate the definite integral $\int_{0}^{1}{\sqrt{1-{{(x-1)}^{2}}}dx}$. The possible answers are:
A) $\dfrac{\pi }{2}$
B) $\dfrac{\pi }{2}-1$
C) $\dfrac{\pi }{4}$
D) $\dfrac{\pi }{2}-\dfrac{1}{2}$

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