
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
Given that the dihedral angle \( \alpha-l-\beta \) has a plane angle of \( 60^{\circ} \), points \( A \) and \( D \) lie on the line \( l \). Ray \( D B \) lies within plane \( \alpha \) and ray \( D C \) lies within plane \( \beta \). It is known that \( \angle B D A = 45^{\circ} \) and \( \angle C D A = 30^{\circ} \). Find \( \cos \angle B D C \).

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