
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 functions $f(x)=x\ln x+2$ and $g(x)=x^{2}-mx$.
(1) Find the minimum value of the function $f(x)$ on the interval $[t,t+2]$ $(t > 0)$.
(2) If there exists $x_{0}\in[ \frac{1}{e},e]$ such that $mf′(x_{0})+g(x_{0})\geqslant 2x_{0}+m$ holds, find the range of values for the real number $m$.

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