
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 $f(x)=x^{2}-(m+1)x+4$.
(I) When $x \in (0,1]$, and $m > 0$, find the minimum value of the function $F(x)=f(x)-(m-1)x$.
(II) If the function $G(x)=2^{f(x)}$ intersects with the line $y=1$ at two distinct points $A(x_{1},1)$, $B(x_{2},1)$ $(0\leqslant x_{1} < x_{2}\leqslant 3)$, find the range of values for the real number $m$.

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