
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 $f(x)=\log_{3}(x-3)+\log_{3}(a-x)$ where $a > 3$.
1. Find the domain of the function $f(x)$.
2. If the function $f(x)$ is monotonic in the interval $(3,6)$, find the range of $a$.
3. When $a=9$, and $f(2x-1) > f(4)$, find the range of the real number $x$.

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