
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 $\overrightarrow{OA} =(3,1)$, $\overrightarrow{OB} =(-1,3)$, and $\overrightarrow{OC} =m\overrightarrow{OA} -n\overrightarrow{OB} (m > 0,n > 0)$, if $m+n=1$, find the minimum value of $|\overrightarrow{OC}|$.

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