
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 \( A\left(x_{1} ; y_{1}\right) \) and \( B\left(x_{2} ; y_{2}\right) \). Find the coordinates of point \( C \) that satisfy the condition: \( (ABC) = \lambda \).

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