
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
A set $M$ consisting of certain integers has the following properties:
(1) $M$ has positive and negative elements;
(2) $M$ has odd and even elements;
(3) $-1 \notin M$;
(4) If $x, y \in M$, then $x+y \in M$.

Examine the relationship between the real numbers 0 and 2 and the set $M$.

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