
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 such that \(\mathbf{a} \cdot \mathbf{b} = 0\), find the largest possible value of:
\[
\|\mathbf{a} - \mathbf{b}\|^2 + \|\mathbf{a} - \mathbf{c}\|^2 + \|\mathbf{b} - \mathbf{c}\|^2.
\]
Note: A unit vector is a vector of magnitude 1.

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