
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, $AC=BC=1$, and $\overrightarrow {CO}=x \overrightarrow {CA}+y \overrightarrow {CB}$ with $x+y=1$. The minimum value of the function $f(m)=| \overrightarrow {CA}-m \overrightarrow {CB}|$ is $\frac { \sqrt {3}}{2}$. Find the minimum value of $| \overrightarrow {CO}|$.

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