
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
A plane passes through the vertices \(A, C,\) and \(D_{1}\) of a rectangular parallelepiped \(A B C D A_{1} B_{1} C_{1} D_{1}\). This plane forms a dihedral angle of \(60^\circ\) with the base plane. The sides of the base are 4 cm and 3 cm. Find the volume of the parallelepiped.

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