
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 set $A = \{x|-2 \leq x \leq 5\}$, and $B = \{x|m + 1 \leq x \leq 2m - 1\}$.
(1) If $B \subseteq A$, find the range of real numbers $m$.
(2) When $x$ belongs to the set of integers $Z$, find the number of non-empty proper subsets of $A$.
(3) When $x$ belongs to the set of real numbers $R$, there is no element $x$ such that $x \in A$ and $x \in B$ hold simultaneously, find the range of real numbers $m$.

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