
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 $f(x)$ whose graph passes through the point $(0,4)$, and for any $x$, it satisfies $f(3-x)=f(x)$, and it has a minimum value of $\frac{7}{4}$.
(Ⅰ) Find the expression of the function $f(x)$;
(Ⅱ) Find the minimum value $g(t)$ of the function $h(x)=f(x)-(2t-3)x$ on the interval $[0,1]$.

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