
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
In the Cartesian coordinate system $xOy$, if the line $l_{1}:kx-y+2=0$ intersects with the line $l_{2}:x+ky-2=0$ at point $P$, then as the real number $k$ varies, the maximum distance from point $P$ to the line $l:x-y-4=0$ is \_\_\_\_.

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