
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 the convex quadrilateral \( ABCD \), angle \( \angle ABD = 65^\circ \), angle \( \angle CBD = 35^\circ \), angle \( \angle ADC = 130^\circ \), and \( AB = BC \). Find the angles of the quadrilateral \( ABCD \).

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