
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
The right-angle coordinates of the points of a line are given by the following expressions:
\[ x = \frac{1-u^{2}-v^{2}}{(1-u)^{2}+v^{2}} \]
\[ y = \frac{2v}{(1-u)^{2}+v^{2}} \]

where \( u \) and \( v \) are parameters and \(\frac{v}{u}=m\), a nonzero constant. Provide the equation of the line in terms of \( x \) and \( y \), and the relationship involving \( m \).

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