
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 proposition $p$: $x > m$ is a necessary condition for $2x-5 > 0$; let proposition $q$: The real number $m$ satisfies the equation $\frac{x^2}{m-1}+\frac{y^2}{2-m}=1$ represents a hyperbola.

(Ⅰ) If "$p \wedge q$" is true, find the range of the real number $m$;

(Ⅱ) If "$p \wedge q$" is false, and "$p \vee q$" is true, find the range of the real number $m$.

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