
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 circle $O$ with a radius of 10, and the length of chord $AB$ is 10.  
(1) Find the size of the central angle $\alpha$ opposite to chord $AB$;  
(2) Calculate the length $l$ of the arc corresponding to angle $\alpha$ and the area $S$ of the sector formed by this arc.

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