
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 that \( AD \), \( BE \), and \( CF \) are the altitudes of an acute triangle \( ABC \). The coordinates of \( D \), \( E \), and \( F \) are \((4, 0)\), \(\left(\frac{80}{17}, \frac{20}{17}\right)\), and \(\left(\frac{5}{2}, \frac{5}{2}\right)\) respectively. Find the coordinates of points \( A \), \( B \), and \( C \).

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