
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
Let $f(x) = x^2 - m \ln(2x + 1)$, where $x \in (- \frac{1}{2}, 1]$, and $m > 0$.
(I) Find the range of values of the real number $m$ such that the function $f(x)$ is decreasing on the interval $(- \frac{1}{2}, 1]$;
(II) Determine whether the function $f(x)$ has a minimum value. If it exists, find the value of $x$ when the minimum value is taken; if not, explain the reason.

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