
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 points $A(4,0)$, $B(0,4)$, and $C(3\cos α,3\sin α)$.
(1) If $α \in (0,π)$, and $| \overrightarrow{AC}|=| \overrightarrow{BC}|$, find the value of $α$;
(2) If $\overrightarrow{AC} \perp \overrightarrow{BC}$, find the value of $\frac{2\sin ^{2}α+\sin 2α}{1+\tan α}$.

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