
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）It is known that the function $f(x)=ax-\frac{b}{x}$, and the tangent line equation of the curve $y=f(x)$ at the point $(2,f(2))$ is $7x-4y-12=0$.
(1) Find the analytical expression of $f(x)$.
(2) The area of the triangle enclosed by the tangent line at any point on the curve $f(x)$, the line $x=0$, and the line $y=x$ is a constant value. Find this constant value.

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