
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
In triangle \(ABC\), perpendiculars are erected on the side \(AB\) at points \(A\) and \(B\), intersecting \(BC\) and \(AC\) at points \(B_1\) and \(A_1\) respectively. What is the area of the triangle if \(AB = c\), \(AB_1 = m\), and \(BA_1 = n\)?


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