
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 \(y \in [0, \pi]\) for which 
\[\sin(x+y) \leq \sin(x) + \sin(y)\]
for every \(x\) between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\), inclusive.

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