
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 a quadratic function $y=f(x)$ has a minimum value of -2, and satisfies $f(3)=f(-1)=2$.  
(1) Find the expression for $f(x)$.  
(2) Solve the inequality $f(2t^2-4t+3) > f(t^2+t+3)$.

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