
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
Let \(AA_1B_1B\) be the axial section of a cylinder, and let \(C\) be a point on the circumference of the base. Given \(AA_1 = 1\), \(AB = 4\), and \(\angle BAC = 60^\circ\), find the dihedral angle between plane \(A_1CB_1\) and the base of the cylinder \(AB\).

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