
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 function $y=f(x)$ that satisfies $f(x-2)=x^2-4x+9$.
(1) Find the explicit formula for $f(x)$;
(2) Let $g(x)=f(x)-bx$, if $g(x)$ attains its maximum value $\frac{11}{2}$ when $x \in \left[\frac{1}{2}, 1\right]$, find the value of $b$.

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