
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
It is known that the numbers \( x, y, z \) form an arithmetic progression with the common difference \(\alpha=\arccos \left(-\frac{1}{5}\right)\), and the numbers \( 2+\sin x, 2+\sin y, 2+\sin z \) form a non-constant geometric progression. Find \(\sin y\).

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