
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
Given propositions $P$: $\frac{x^2}{m-1} + \frac{y^2}{m-4} = 1$ represents a hyperbola, and $Q$: $\frac{x^2}{m-2} + \frac{y^2}{4-m} = 1$ represents an ellipse.  
(1) If both propositions $P$ and $Q$ are true, then what kind of condition is $P$ for $Q$?  
(Please briefly explain if it is a "sufficient but not necessary condition," a "necessary but not sufficient condition," a "necessary and sufficient condition," or "neither sufficient nor necessary condition").  
(2) If the compound proposition $P \land Q$ is false, and $P \lor Q$ is true, find the range of the real number $m$.

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