
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 rectangular parallelepiped \(ABCD A_{1} B_{1} C_{1} D_{1}\), the lengths of the edges are known: \(AB = a\), \(AD = b\), \(AA_{1} = c\).

a) Find the angle between the planes \(BB_{1}D\) and \(ABC_{1}\).

b) Find the angle between the planes \(AB_{1}D_{1}\) and \(A_{1}C_{1}D\).

c) Find the angle between the line \(BD_{1}\) and the plane \(A_{1}BD\).

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