
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
Let $α$ and $β$ be angles in the range $[0,π]$, and they satisfy $\sin α \cos β - \cos α \sin β = 1$. What is the range of possible values for $\cos (2α - β)$?

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