
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, given points $A(a+1,-3)$ and $B(3,2a+1)$.  
$(1)$ If point $A$ lies on the $y$-axis, find the coordinates of point $B$.  
$(2)$ If the line segment $AB$ is parallel to the $x$-axis, find the value of $a$.

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