
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 that the vertex $B(3,2)$ of $\triangle ABC$ and the equation of the altitude on side $AB$ is $x-2y+2=0$.
$(1)$ Find the general equation of line $AB$.
$(2)$ Choose one of the following conditions and find the general equation of line $AC$.
① The equation of the angle bisector of angle $A$ is $x+y-2=0$.
② The equation of the median on side $BC$ is $10x+11y-16=0$.
(Note: If multiple conditions are chosen and answered separately, the first answer will be scored.)

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