
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
In the Cartesian coordinate system, the coordinates of point $P$ are $\left(a-7,3-2a\right)$. Point $P$ is moved $4$ units up and then $5$ units to the right to obtain point $Q$.<br/>$(1)$ If point $Q$ is located in the first quadrant, find the range of values for $a$.<br/>$(2)$ Under the condition in $(1)$, if $a$ is an integer, determine the coordinates of points $P$ and $Q$.

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