
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 \( x > 0 \), \( y \geq 0 \), and \( x + 2y = \frac{1}{2} \), find the values of \( x \) and \( y \) that maximize and minimize \( u = \log_{0.75}(8xy + 4y^2 + 1) \), and determine the maximum and minimum values.

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