
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 $A$, $B$, $C$ with coordinates $(4,0)$, $(0,4)$, $(3\cos \alpha,3\sin \alpha)$ respectively, and $\alpha\in\left( \frac {\pi}{2}, \frac {3\pi}{4}\right)$. If $\overrightarrow{AC} \perp \overrightarrow{BC}$, find the value of $\frac {2\sin ^{2}\alpha-\sin 2\alpha}{1+\tan \alpha}$.

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