
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 vertices of triangle $\triangle ABC$ are $B(-2,0)$ and the equation of the altitude on side $AB$ is $x+3y-26=0$. Find:<br/>
$(1)$ The equation of line $AB$;<br/>
$(2)$ Choose one of the following conditions and complete the question:<br/>
① The equation of the angle bisector of angle $A$ is $x+y-2=0$;<br/>
② The equation of the median on side $BC$ is $y=3$.<br/>
If ____, find the equation of line $AC$.<br/>
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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