
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 $f(x) = (1+x)^{2} - 2\ln (1+x)$.
(I) For any $x_{0} \in [0,1]$, the inequality $f(x_{0}) - m \leqslant 0$ always holds. Find the minimum value of the real number $m$.
(II) If there exists an $x_{0} \in [0,1]$ such that the inequality $f(x_{0}) - m \leqslant 0$ holds, find the range of values of the real number $m$.

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