
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 circle $C$: $x^{2}+y^{2}-6x-4y+4=0$, the midpoint of the chord intercepted by line $l_{1}$ on the circle is $P(5,3)$.
(1) Find the equation of line $l_{1}$;
(2) If line $l_{2}:x+y+b=0$ intersects with circle $C$, find the range of $b$.

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