
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 \(a_{0}, a_{1}, \cdots, a_{n}, \cdots\) that satisfies \((3 - a_{n+1})(6 + a_{n}) = 18\) with \(a_{0} = 3\), find the value of \(\sum_{i=0}^{n} \frac{1}{a_{i}}\).

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