
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  $ABCD$ , point  $X$  is selected on side  $AD$ , and the diagonals intersect at point  $E$ . It is known that  $AC = BD$ ,  $\angle ABX = \angle AX B = 50^o$ ,  $\angle CAD = 51^o$ ,  $\angle AED = 80^o$ . Find the value of angle  $\angle AXC$ .


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