
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 $A(-1,0)$ and $B(1,0)$, lines $AM$ and $BM$ intersect at point $M$, and the ratio of the slope of line $AM$ to the slope of line $BM$ is $3$. Then, the trajectory of point $M$ is __________.

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