
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\\), and \\(C\\) with coordinates \\(A(3,0)\\), \\(B(0,3)\\), and \\(C(\\cos α,\\sin α)\\) respectively, where \\(α∈\\left( \\dfrac{π}{2}, \\dfrac{3π}{2}\\right) \\).

\\((1)\\) If \\(\\left| \\overrightarrow{AC}\\right|=\\left| \\overrightarrow{BC}\\right| \\), find the value of angle \\(α\\).

\\((2)\\) If \\( \\overrightarrow{AC}· \\overrightarrow{BC}=-1 \\), find the value of \\( \\dfrac{2{\\sin }^{2}α+\\sin 2α}{1+\\tan α} \\).

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