
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 point $A(1,-2)$ and vector $\vec{a}=(2,3)$,

$(1)$ If vector $\vec{AB}$ is in the same direction as vector $\vec{a}$ and $|\vec{AB}|=2\sqrt{13}$, find the coordinates of point $B$;

$(2)$ If the angle between vector $\vec{a}$ and vector $\vec{b}=(-3,k)$ is obtuse, find the range of the real number $k$.

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