
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 $\lambda \in R$, the moving line $l_{1}$: $\lambda x-y+\lambda =0$ passes through the fixed point $A$, the moving line $l_{2}$: $x+\lambda y-3-2\lambda =0$ passes through the fixed point $B$. If $P$ is the intersection point of $l_{1}$ and $l_{2}$, find the maximum value of $|PA|\cdot |PB|$.

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