
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 a regular tetrahedron $\mathrm{ABCD}$ with edge length 2, the angle $\theta$ between edge $\mathrm{AD}$ and plane $\alpha$ satisfies $\theta \in \left[\frac{\pi}{3}, \frac{\pi}{2}\right]$. Vertex $\mathrm{A}$ lies in plane $\alpha$, while vertices $\mathrm{B}$, $\mathrm{C}$, and $\mathrm{D}$ are outside $\alpha$. Determine the range of distances from the midpoint $\mathrm{E}$ of edge $\mathrm{BC}$ to plane $\alpha$.

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