
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
Let points A(3,0), B(0,3), and C(cosα, sinα).
1. If $\overrightarrow{AC} \cdot \overrightarrow{BC} = -1$, find the value of $\sin\left(\alpha + \frac{\pi}{4}\right)$.
2. Let O be the origin of the coordinate system. If $|\overrightarrow{OA} - \overrightarrow{OC}| = \sqrt{13}$ and $\alpha \in (0, \pi)$, find the angle between $\overrightarrow{OB}$ and $\overrightarrow{OC}$.

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