
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 rhombus \(ABCD\), \(\angle DAB = 60^\circ\). Fold \(\triangle ABD\) along \(BD\) to obtain \(\triangle A_1BD\). If the dihedral angle \(A_1 - BD - C\) is \(60^\circ\), then find the cosine of the angle formed by the skew lines \(DA_1\) and \(BC\).

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