
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 cube \(A B C D A_{1} B_{1} C_{1} D_{1}\) (where \(A A_{1} \parallel B B_{1} \parallel C C_{1} \parallel D D_{1}\)), a plane is drawn through the midpoints of the edges \(D D_{1}\) and \(D_{1} C_{1}\) and vertex \(A\). Find the angle between this plane and the face \(A B C D\).

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