
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 proposition P: The curve represented by the equation $$\frac {x^{2}}{4-t}+ \frac {y^{2}}{t-1}=1$$ is an ellipse with foci on the x-axis; proposition Q: The inequality involving real number t is $t^2-(a+3)t+(a+2)<0$.  
(1) If proposition P is true, find the range of real number t;  
(2) If proposition P is the sufficient but not necessary condition for proposition Q, find the range of real number a.

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