
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 \(ABCD A_1 B_1 C_1 D_1\), two diagonals of the side faces \(A_1 C_1\) and \(C_1 D\) are drawn. Find the angle between them, given that the diagonal \(A_1 C_1\) is equal in length to one of the edges of the parallelepiped, and the diagonal \(C_1 D\) forms a 30-degree angle with the same edge.

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