
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
A moving line $l: (3\lambda+1)x + (1-\lambda)y + 6 - 6\lambda = 0$ passes through a fixed point $P$. The coordinates of point $P$ are \_\_\_\_\_\_, and if line $l$ intersects the positive half of the x-axis, then the range of $\lambda$ is \_\_\_\_\_\_.

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