
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 that the line \( l \) is tangent to the parabola \( y = \frac{1}{2} x^2 \) and intersects the circle \( x^2 + y^2 = 1 \) at points \( A \) and \( B \). Let \( M \) be the midpoint of \( AB \), and \( E(0, -\frac{1}{2}) \). Find the range of values for \( |EM| \).

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