
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 $$|\overrightarrow{OA}|=4, |\overrightarrow{OB}|=2, \angle AOB= \frac{2\pi}{3}, \overrightarrow{OC}=x\overrightarrow{OA}+y\overrightarrow{OB}$$, and $x+2y=1$, the minimum value of $$|\overrightarrow{OC}|$$ is \_\_\_\_\_\_.

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