
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
(The full score for this question is 12 points) Given a cube with edge length 1, where AC1, E, and F are the midpoints of B1C1 and C1D1, respectively.  
(1) Find the distance from point A1 to the plane BDFE.  
(2) Find the angle between line A1D and plane BDFE.

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