
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 $m\in\mathbb{R}$, if point $M(x,y)$ is the intersection of line $l_{1}: my=-x$ and line $l_{2}: mx=y+m-3$, and $l_{1}$ and $l_{2}$ respectively pass through fixed points $A$ and $B$, then the maximum value of $|MA|\cdot|MB|$ is ______.

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