
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 that the coordinates of points A and B are (-1, 0) and (1, 0) respectively, lines AM and BM intersect at point M, and the ratio of the slope of line AM to the slope of line BM is 2. Find the equation of the trajectory of point M.

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