
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 acute \\(\triangle ABC\\), \\(AC=BC=2\\), and \\(\overrightarrow{CO}=x\overrightarrow{CA}+y\overrightarrow{CB}\\) (where \\(x+y=1\\)), the minimum value of the function \\(f(\lambda )=|\overrightarrow{CA}-\lambda \overrightarrow{CB}|\\) is \\(\sqrt{3}\\). Find the minimum value of \\(|\overrightarrow{CO}|\).

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