
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
Define a sequence \(a_n\) by \(a_0 = 0\) and \(a_{n+1} = 1 + \sin(a_n - 1)\). Find \(\lim \left(\frac{\sum_{i=0}^n a_i}{n}\right)\).

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