
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 that $y=f(x)$ is a linear function, and it satisfies $f[f(x)]=16x-15$, find the expression for $f(x)$.

(2) If the function $f(x)=\frac{(x+1)(x+a)}{x}$ is an odd function, then the real number $a=$ ______.

(3) Given the function $f(x)=x+\sqrt{2x-1}$, find the minimum value of $f(x)$.

(4) If the set $A=\{ x|ax^2+3x+2=0 \}$ has at most one element, then the range of the real number $a$ is ______.

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