
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 $l_1: ax+y-1=0$ and $l_2: (3a-4)x-y-2=0$, and $l_1 \parallel l_2$

(1) Find the value of $a$  
(2) Find the equation of the circle with center $N(1,1)$ that is tangent to $l_2$.

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