
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 point $A\left(3a-9,2a-10\right)$, solve the following problems:<br/>$(1)$ If the coordinates of point $B$ are $\left(4,5\right)$, and $AB$<span class="special-symbol">∥</span>$y$ axis, find the value of $a$;<br/>$(2)$ If point $A$ is in the fourth quadrant, and $a$ is an integer, find the coordinates of point $A$.

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