
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
 $ABC$  is triangle.  $l_1$ - line passes through  $A$  and parallel to  $BC$ ,  $l_2$  -  line passes through  $C$  and parallel to  $AB$ . Bisector of  $\angle B$  intersect  $l_1$  and  $l_2$  at  $X,Y$ .  $XY=AC$ . What  value can take  $\angle A- \angle C$  ?

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