
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 a triangle with vertices \( A(1,-1), B(-2,1), C(3,-5) \). Write the equation of the perpendicular from vertex \( A \) dropped onto the median drawn from vertex \( B \).

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