
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
Find all \(y \in [0, 2\pi]\) for which \[\cos(x - y)\geq \cos(x) - \cos(y)\] for every \(x\) between \(0\) and \(2\pi\), inclusive.

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