
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 $f(x)=x^{2}+bx+b\sqrt{1-2x}$ $(b\in\mathbb{R})$.

(1) When $b=4$, find the extreme values of $f(x)$;

(2) If $f(x)$ is monotonically increasing in the interval $\left(0, \frac{1}{3}\right)$, find the range of values for $b$.

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