
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
A sequence  $a_0,a_1,a_2,\cdots,a_n,\cdots$  satisfies that  $a_0=3$ , and  $(3-a_{n-1})(6+a_n)=18$ , then the value of  $\sum_{i=0}^{n}\frac{1}{a_i}$  is________.

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