
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 $f(x)=m\ln x+nx$ at the point $(1,f(1))$, its tangent line is parallel to the line $x+y-2=0$, and $f(1)=-2$, where $m$, $n\in R$.
(I) Find the values of $m$ and $n$, and determine the monotonic intervals of the function $f(x)$;
(II) Let the function $g(x)= \frac{1}{t}(-x^{2}+2x)$, for positive real numbers $t$, if there exists $x_{0}\in[1,e]$ such that $f(x_{0})+x_{0}\geqslant g(x_{0})$ holds, find the maximum value of $t$.

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