
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 a regular tetrahedron \( P-ABC \) with edge length 1, where \( D \) is the midpoint of \( PC \), and \( E \) is a moving point on the segment \( AD \). Find the range of possible values for the angle between line \( BE \) and plane \( ABC \).

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