
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 the region enclosed by the curve $y= \sqrt {1-(x-1)^{2}}$ and the $x$-axis be denoted as $D$. If the curve $y=ax(x-2) (a < 0)$ divides the area of $D$ into two equal parts, calculate the value of $a$.

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