
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 vectors $|\vec{OA}|=3$, $|\vec{OB}|=2$, and $\vec{OC}=m\vec{OA}+n\vec{OB}$, if the angle between $\vec{OA}$ and $\vec{OB}$ is $60^{\circ}$, and $\vec{OC} \perp \vec{AB}$, then the value of the real number $\frac{m}{n}$ is ______.

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