
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
Let $m \in \mathbb{R}$, and consider a dynamic line $l_1$ passing through a fixed point $A$ with the equation $l_1$: $x + my = 0$, and another dynamic line $l_2$ passing through a fixed point $B$ with the equation $l_2$: $mx - y - m + 3 = 0$. If the intersection point of $l_1$ and $l_2$ is $P(x, y)$,  
(I) Determine the positional relationship between $l_1$ and $l_2$;  
(II) Find the maximum value of $|PA| \cdot |PB|$.

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