
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 two lines $l_{1}: x-2y+3=0$ and $l_{2}: x+2y-9=0$, their intersection point is $A$.
$(1)$ Find the equation of the line that passes through point $A$ and is parallel to the line $2x+3y-1=0$;
$(2)$ Find the equation of the line that passes through point $A$ and has a slope angle twice that of line $l_{1}$.

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