
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
(1) Given $f(x-2)=3x-5$, find $f(x)$;
(2) Given a quadratic function $f(x)$ whose graph passes through the point $(0,4)$, satisfies $f(3-x)=f(x)$ for any $x$, and has a minimum value of $\frac{7}{4}$, find the analytic expression of $f(x)$.

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