
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 same plane, the magnitudes of vectors $\overrightarrow{OA}$, $\overrightarrow{OB}$, and $\overrightarrow{OC}$ are $1$, $2$, and $3$, respectively. The angle between $\overrightarrow{OA}$ and $\overrightarrow{OC}$ is $\alpha$, with $\cos \alpha= \frac {1}{3}$. The angle between $\overrightarrow{OB}$ and $\overrightarrow{OC}$ is $60^{\circ}$. If $\overrightarrow{OC}=m \overrightarrow{OA}+n \overrightarrow{OB}$ $(m,n\in\mathbb{R})$, then $m+3n=$ ______．

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