
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
The sequence \( a_{0}, a_{1}, a_{2}, \cdots, a_{n}, \cdots \) satisfies the relationship \( \left(3-a_{n+1}\right)\left(6+a_{n}\right)=18 \) and \( a_{0}=3 \). Find \( \sum_{i=0}^{n} \frac{1}{a_{i}}=\ ?\ \)

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