
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
In the Cartesian coordinate system, there are three points A(0, -1), B(1, 3), C(2, 6). It is known that on the line $y = ax + b$, the points with abscissas 0, 1, 2 are respectively D, E, F. Find the values of $a$ and $b$ that minimize $AD^2 + BE^2 + CF^2$.

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