
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 equation of the line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ can be represented as $\frac {x-x_{1}}{x_{2}-x_{1}} = \frac {y-y_{1}}{y_{2}-y_{1}}$ and $\frac {x-x_{2}}{x_{1}-x_{2}} = \frac {y-y_{2}}{y_{1}-y_{2}}$ and $(y-y_{1})(x_{2}-x_{1})=(x-x_{1})(y_{2}-y_{1})$ and $y-y_{1}= \frac {y_{2}-y_{1}}{x_{2}-x_{1}}$.

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