
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 \( x \geq 0 \) and \( y \geq 0 \), and \( x^{2} + y^{2} = 4 \), find the minimum value of \( xy - 4(x + y) - 2 \).

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