
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
In the xy-plane with a rectangular coordinate system, the terminal sides of angles $\alpha$ and $\beta$ intersect the unit circle at points $A$ and $B$, respectively.
1. If point $A$ is in the first quadrant with a horizontal coordinate of $\frac{3}{5}$ and point $B$ has a vertical coordinate of $\frac{12}{13}$, find the value of $\sin(\alpha + \beta)$.
2. If $| \overrightarrow{AB} | = \frac{3}{2}$ and $\overrightarrow{OC} = a\overrightarrow{OA} + \overrightarrow{OB}$, where $a \in \mathbb{R}$, find the minimum value of $| \overrightarrow{OC} |$.

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