
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 $f(x)=x^{2}-4x+a+3$ and $g(x)=mx+5-2m$,
(1) When $a=-3$ and $m=0$, find the solutions to the equation $f(x)-g(x)=0$;
(2) Find the range of real number values of $a$ such that the equation $f(x)=0$ has real roots in the interval $[-1,1]$;
(3) When $a=0$, find the range of real number values of $m$ such that for any $x_{1}∈[1,4]$, there exists $x_{2}∈[1,4]$ that makes $f(x_{1})=g(x_{2})$ hold.

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