
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: $x^2+y^2-6x-4y+10=0$, and two lines $l_1$: $y=kx$, $l_2$: $3x+2y+10=0$.
(1) Find the range of $k$ such that $l_1$ intersects circle C at two points A and B.
(2) Let P be the midpoint of AB, and Q be the intersection point of $l_1$ and $l_2$. Find the value of $|OP| \cdot |OQ|$.

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