
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 that $\alpha, \beta \in \mathbf{R}$, the lines $\frac{x}{\sin \alpha+\sin \beta}+\frac{y}{\sin \alpha+\cos \beta}=1$ and $\frac{x}{\cos \alpha+\sin \beta}+\frac{y}{\cos \alpha+\cos \beta}=1$ intersect on the line $y=-x$, find the value of $\sin \alpha+\cos \alpha+\sin \beta+\cos \beta$.

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