
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 $xOy$, given points $A(-2,2)$ and $B(2,6)$, a line $l$ passes through the point $(0, m)$ and is tangent to the unit circle $x^2 + y^2 = 1$ at all times. There are exactly two points $P$ that satisfy:
① $\vec{PA} \cdot \vec{PB} = -4$
② The distance from point $P$ to line $l$ is 1
Find the range of values for the real number $m$.

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