
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 the function $f(x) = x^2 - (a+1)x + b$,  
(1) If $b = -1$, the function $y=f(x)$ has one root in the interval $x \in [2, 3]$. Find the range of values for $a$.  
(2) If $a=b$, and $\forall a \in [2, 3]$, $f(x) < 0$ holds true, determine the range of $x$.

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