
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 $\alpha, \beta \in \mathbb{R}$, 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 $y=-x$. Find the value of $\sin\alpha+\cos\alpha+\sin\beta+\cos\beta$.

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