
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 $A(3,0)$, $B(0,3)$, and $C(\cos α, \sin α)$.

(1) If $\overrightarrow{AC} \cdot \overrightarrow{BC} = -1$, find the value of $\sin \left( α + \frac{π}{4} \right)$.

(2) If $| \overrightarrow{OA} + \overrightarrow{OC} | = \sqrt{13}$ and $α \in (0, π)$, find the angle between $\overrightarrow{OB}$ and $\overrightarrow{OC}$.

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