
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 points $A(2,0)$ and $B(-2,0)$; line $l: (1+3\lambda)x - (1+2\lambda)y + 2 = 0$ (where $\lambda \in \mathbb{R}$). Find the possible values of the slope $k$ of line $l$ if it has a common point with line segment $AB$.

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