
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 \( x, y \in \mathbb{R}^{+} \), find the minimum value of the function:
\[ f(x, y) = \sqrt{x^{2} - 3x + 3} + \sqrt{y^{2} - 3y + 3} + \sqrt{x^{2} - \sqrt{3}xy + y^{2}}. \]

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