
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
Suppose that there are two triangles $\triangle ABC$ and $\triangle ACD$, where $AB = AC = AD$ in $\triangle ABC$. In $\triangle ACD$, $AC = AD$, but $CD = 2 \cdot AC$. If $\angle BAC = 30^\circ$, determine $\angle BDC$.

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