
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 sides \( AD \) and \( DC \) of an inscribed quadrilateral \( ABCD \) are equal. Point \( X \) is marked on side \( BC \) such that \( AB = BX \). It is known that \( \angle B = 34^\circ \) and \( \angle XDC = 52^\circ \).

(a) (1 point) How many degrees is angle \( AXC \) ?

(b) (3 points) How many degrees is angle \( ACB \) ?

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