
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 that point $A$, $B$, $C$ have coordinates $A(3,0)$, $B(0,3)$, and $C(\cos\alpha, \sin\alpha)$ respectively, where $\alpha \in \left(\frac{\pi}{2}, \frac{3\pi}{2}\right)$. If the vector $\overrightarrow{OC}$ is parallel to the vector $\overrightarrow{AB}$, and $O$ is the origin of the coordinate system, then the value of angle $\alpha$ is __________.

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