
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 the function $f(x) = x^2 - m\ln(2x+1)$, where $x \in \left(-\frac{1}{2}, 1\right]$, and $m > 0$.

(I) If the function $f(x)$ is a decreasing function on the interval $\left(-\frac{1}{2}, 1\right]$, find the range of values for the real number $m$.

(II) Does the function $f(x)$ have a minimum value? If it exists, find the value of $x$ when $f(x)$ takes its minimum value; if not, please explain why.

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