
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
Consider the line $10x + 8y = 80$ forming a triangle with the coordinate axes. Calculate the sum of the lengths of the altitudes of this triangle.
A) $\frac{58}{\sqrt{41}}$
B) $\frac{58}{41}$
C) $\frac{18\sqrt{41} + 40}{\sqrt{41}}$
D) $28$

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