
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(1,0), B(0,2), and C(cosα, sinα), where (0 < α < π).
(Ⅰ) If $|\vec{OA} + \vec{OC}| = \sqrt{2 + \sqrt{3}}$ (O is the origin of coordinates), find the angle between $\vec{OB}$ and $\vec{OC}$;
(Ⅱ) If $\vec{AC} \perp \vec{BC}$, find the value of $3\sin\alpha - \cos\alpha$.

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