
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
If $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{c}$ are unit vectors in $\mathbb{R}^3$, find the smallest possible value of
\[
\|\mathbf{a} - \mathbf{b}\|^2 + \|\mathbf{b} - \mathbf{c}\|^2 + \|\mathbf{c} - \mathbf{a}\|^2.
\]

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