
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 the points $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ lie on the line $y = 2mx + m + 1$, find the perimeter of the triangle formed by these points in terms of $x_1, x_2, x_3,$ and $m$.

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