
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 equation $15x + 8y = 120$ forms a triangle with the coordinate axes. Determine the sum of the lengths of the altitudes of this triangle.
A) $\frac{360}{17}$
B) $\frac{391}{17}$
C) $\frac{107}{5}$
D) $\frac{43}{2}$
E) $\frac{281}{13}$

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