
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
Given a line in the coordinate plane that intersects the x-axis at point A(3, 0) and the y-axis at point B(0, 3), and a point C(cosα, sinα), where $\frac{\pi}{2} < \alpha < \frac{3\pi}{2}$.
(1) If $|\overrightarrow{AC}| = |\overrightarrow{BC}|$, find the value of α;
(2) If $\overrightarrow{AC} \cdot \overrightarrow{BC} = -1$, find the value of sin2α.

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