
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
(1) Find the maximum distance from point P to the line $x - y - 4 = 0$ as the real number $k$ varies, given that lines $l_1: kx - y + 2 = 0$ and $l_2: x + ky - 2 = 0$ intersect at point P.

(2) Given points $A(-2, -2)$, $B(-2, 6)$, and $C(4, -2)$, and point $P$ that satisfies $x^2 + y^2 = 4$, find the maximum and minimum values of $|PA|^2 + |PB|^2 + |PC|^2$.

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