
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 a regular quadrilateral prism \( ABCDA_1B_1C_1D_1 \) \( (A \| A_1 \| B \| B_1 \| C \| C_1 \| D \| D_1 ) \), a plane passes through the midpoints of two adjacent sides of the base \( DC \) and \( AD \), and the vertex \( B_1 \) of the upper base. Find the angle between this plane and the base plane if the perimeter of the cross-section is three times the diagonal of the base.

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