
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 a line $l$ that passes through the point $(0, 1)$ with the equation $l: x\tan\alpha - y - 3\tan\beta = 0$ and a normal vector of $(2, -1)$, find the value of $\tan(\alpha+\beta)$.

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