
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 that the coordinates of points $A$, $B$, and $C$ are $A(3,0)$, $B(0,3)$, and $C(\cos α, \sin α)$, respectively.
1. If $| \overrightarrow{AC}|=| \overrightarrow{BC}|$, find the value of angle $α$.
2. If $ \overrightarrow{AC} \cdot \overrightarrow{BC}=-1$, find the value of $\frac{2\sin ^{2}α+2\sin α\cos α}{1+\tan α}$.

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