
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 $A(3,0)$, $B(0,3)$, $C(\cos\alpha,\sin\alpha)$, where $\alpha\in\left(\frac{\pi}{2},\frac{3\pi}{2}\right)$. If $\overrightarrow{AC}\cdot\overrightarrow{BC}=-1$, then $\frac{2\sin^2\alpha+\sin2\alpha}{1+\tan\alpha}=$____.

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