
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 a parallelogram \(A B C D\). It is known that the centers of the circumcircles of triangles \(A B C\) and \(C D A\) lie on the diagonal \(B D\). Find the angle \(D B C\) if \(\angle A B D = 35^\circ\).

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