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

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