
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
Let  $M$  be a set and  $A,B,C$  given subsets of  $M$ . Find a necessary and sufficient condition for the existence of a set  $X\subset M$  for which  $(X\cup A)\backslash(X\cap B)=C$ . Describe all such sets.

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