
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
Given \(\alpha, \beta \in \mathbf{R}\), the intersection point of the lines \(\frac{x}{\sin \alpha+\sin \beta} + \frac{y}{\sin \alpha+\cos \beta} = 1\) and \(\frac{x}{\cos \alpha+\sin \beta} + \frac{y}{\cos \alpha+\cos \beta} = 1\) lies on the line \(y = -x\). Calculate \(\sin \alpha + \cos \alpha + \sin \beta + \cos \beta\).

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