
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 $m \in \mathbb{R}$, a moving line passing through a fixed point A is given by $x + my = 0$, and another moving line passing through a fixed point B is given by $mx - y - m + 3 = 0$. These two lines intersect at point P $(x, y)$. Find the maximum value of $|\overrightarrow{PA}| \cdot |\overrightarrow{PB}|$.

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