
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 parallelogram \(ABCD\), the angle \( \angle ACD \) is \(30^{\circ}\). It is known that the centers of the circumcircles of triangles \(ABD\) and \(BCD\) are located on the diagonal \(AC\). Find the angle \( \angle ABD \).

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