
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
If the coordinates of point $P(x,y)$ satisfy the system of equations $\left\{\begin{array}{l}{x+y=2a-b-4}\\{x-y=b-4}\end{array}\right.$.<br/>$(1)$ When $a=1$ and $b=2$, find the coordinates of point $P$;<br/>$(2)$ If point $P$ is in the second quadrant, and there are only four integers that satisfy the requirement for $a$, find the range of values for $b$;<br/>$(3)$ If the equation about $z$, $yz+x+4=0$, has a unique solution $z=2$, find the solution set for the inequality about $t$, $at \gt b$.

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