
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 coordinates of vertex $B$ of triangle $\triangle ABC$ are $\left(1,-2\right)$, the equation of the median $CM$ on side $AB$ is $2x-y+1=0$, and the equation of the angle bisector of $\angle BAC$ is $x+7y-12=0$.<br/>$(1)$ Find the coordinates of point $A$;<br/>$(2)$ Find the equation of line $AC$.

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