
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(3cosα, 3sinα),
(1) If α is in the interval (0, π) and |$\overrightarrow{AC}$| = |$\overrightarrow{BC}$|, find the value of α;
(2) If $\overrightarrow{AC} \bot \overrightarrow{BC}$, find the value of $\frac{2\sin^2α + \sin 2α}{1 + \tan α}$.

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