
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
A student wrote the following incorrect formulas for the sine and cosine of a sum: 
$$\sin (\alpha+\beta) = \sin \alpha + \sin \beta$$ 
and 
$$\cos (\alpha+\beta) = \cos \alpha + \cos \beta.$$ 
In his defense, he claimed that for certain values of $\alpha$ and $\beta$, his formulas are nonetheless correct. Find all such pairs $(\alpha, \beta)$.

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