
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
Let \( x, y \in \mathbf{R} \). Find the minimum value of the function \( f(x, y) = x^2 + 6y^2 - 2xy - 14x - 6y + 72 \), and determine the values of \( x \) and \( y \) at which this minimum value is attained.

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