
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
A line \(10x + 4y = 40\) forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle?
**A**) \(14\)   
**B**) \(\frac{120}{12.65}\)   
**C**) \(20\)   
**D**) \(\frac{140}{\sqrt{116}} + 4\)  
**E**) \(14 + \frac{40}{12.65}\)

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