
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 coordinate plane, point $A$ is marked. Point $B$ is marked on the $Ox$ axis, and point $C$ is marked on the $Oy$ axis.

It is known that the equations of the lines $AB$, $BC$, and $AC$ in some order are $y=ax+4$, $y=2x+b$, and $y=\frac{a}{2}x+8$ for some real numbers $a$ and $b$.

Find the sum of the coordinates of point $A$. Specify all possible values.

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