
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 tetrahedron $A B C D$ has one edge $D A$ that is perpendicular to the base $A B C$. Additionally, the angles between the edges meeting at vertex $D$ are given: $A D B = 30^{\circ}$, $B D C = 45^{\circ}$, and $C D A = 60^{\circ}$. Construct (with usual planar steps) the angle $B A C$.

Second-year students should also calculate the angle $B A C$.

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