
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 \( x = \sin \alpha \) and \( y = \sin \beta \), the expression
\[ 
z = \sin (\alpha + \beta) 
\]
generally has four different possible values. Write an equation relating \( x \), \( y \), and \( z \) without involving radicals or trigonometric functions. Also, find the values of \( x \) and \( y \) for which \( z = \sin (\alpha + \beta) \) has fewer than four values.

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