
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 $f(x) = \frac{1}{2}x^{2} + mx + m \ln x$.
(Ⅰ) Discuss the monotonicity of the function $f(x)$;
(Ⅱ) When $m > 0$, if for any two real numbers $x_1$ and $x_2$ in the interval $[1,2]$ with $x_1 < x_2$, the inequality $|f(x_1) - f(x_2)| < x_{2}^{2} - x_{1}^{2}$ holds, find the maximum value of the real number $m$.

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