
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 $f(x) = \log_a x + x - b$ ($a > 0$ and $a \neq 1$). When $2 < a < 3 < b < 4$, the zero of the function $f(x)$, denoted as $x_0$, belongs to the interval $(n, n+1)$, where $n \in \mathbb{N}^*$. Find the value of $n$.

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