
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 sequence $a_0$, $a_1$, $a_2$, ..., $a_n$, ... satisfying the relation $(3-a_{n+1})(6+a_n)=18$, and $a_0 \neq 3$, find the value of $a_n$.

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