
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
We define the sequence \( a_{0}, a_{1}, \ldots \) starting from an arbitrary value \( a_{0} \) using the recursion formula \( a_{n+1} = \sin a_{n} \). Does this sequence converge, and if so, what is its limit?

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