
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 that $\overset{→}{a}, \overset{→}{b}, \overset{→}{c}$ are unit vectors, and $\overset{→}{a} \cdot \overset{→}{b} = 0$, find the minimum value of $(\overset{→}{a} - \overset{→}{c}) \cdot (\overset{→}{b} - \overset{→}{c})$.

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