
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 the coordinates of A, B, C are A(4, 0), B(0, 4), C(3cosα, 3sinα) respectively.  
(1) If α∈(-π, 0) and $|\overrightarrow{AC}|=|\overrightarrow{BC}|$, find the value of angle α;  
(2) If $\overrightarrow{AC} \perp \overrightarrow{BC}$, find the value of $\frac{2\sin^{2}\alpha+\sin2\alpha}{1+\tan\alpha}$.

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