
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), where α ∈ (0, 2π).
1. If $|\overrightarrow{AC}|$ = $|\overrightarrow{BC}|$, find the value of angle α.
2. If $\overrightarrow{AC} \cdot \overrightarrow{BC}$ = 0, find the value of $\frac{\sin ^{2} \alpha+\sin \alpha+\cos \alpha}{2+2 \tan \alpha}$.

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