
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),
(1) If α is in the interval (-π, 0) and the vector magnitude $|\vec{AC}| = |\vec{BC}|$, determine the value of α;
(2) If the dot product of vectors $\vec{AC} \cdot \vec{BC} = 0$, find the value of $\frac{2\sin^2α + 2\sinα\cosα}{1+\tanα}$.

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