
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
The lower base of a quadrilateral truncated pyramid is a rhombus $ABCD$, where $AB=4$ and $\angle BAD=60^\circ$. The edges $AA_1, BB_1, CC_1, DD_1$ are the lateral edges of the truncated pyramid. The edge $A_1B_1=2$, the edge $CC_1$ is perpendicular to the base plane and equals 2. A point $M$ is taken on the edge $BC$ such that $BM=3$. A plane is passed through the points $B_1$, $M$, and the center of the rhombus $ABCD$. Find the dihedral angle between this plane and the plane $AA_1C_1C$.

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