
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 point $P(-2,-1)$, find the maximum distance from $P$ to the line $l: (1+3\lambda)x + (1+\lambda)y - 2 - 4\lambda = 0 (\lambda \in \mathbb{R})$ and the equation of the line at that time.

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