
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
If $x_0 \in \mathbb{R}$ satisfies $f(x_0) = x_0$, then $x_0$ is called a fixed point of $f(x)$.  
(1) If the function $f(x) = x^2 + ax + a$ has no fixed point, find the range of the real number $a$.  
(2) If the fixed point $x_0$ of the function $f(x) = -\ln(x) + 3$ belongs to $[n, n+1)$, where $n \in \mathbb{Z}$, find the value of $n$.

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