
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 $\overset{→}{a}, \overset{→}{b}$ that satisfy $|\overset{→}{a}|=|\overset{→}{b}|=\overset{→}{a}·\overset{→}{b}=2$ and $(\overset{→}{a}-\overset{→}{c})·(\overset{→}{b}-\overset{→}{c})=0$, find the minimum value of $|2\overset{→}{b}-\overset{→}{c}|$.

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