
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 the function f(x) = (x² + bx + b) • $\sqrt{1 - 2x}$ (b ∈ R).
1. Find the extreme values of f(x) when b = 4.
2. Find the range of b values if f(x) is monotonically increasing in the interval (0, $\frac{1}{3}$).

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