
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 $\triangle ABC$, $\angle ACB$ is an obtuse angle, $AC=BC=1$, $\overrightarrow{CO}=x \overrightarrow{CA}+y \overrightarrow{CB}$ and $x+y=1$, the minimum value of the function $f(m)=| \overrightarrow{CA}-m \overrightarrow{CB}|$ is $\frac{\sqrt{3}}{2}$, then the minimum value of $| \overrightarrow{CO}|$ is _______.

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