
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
Find the sum of the lengths of the altitudes of the triangle formed by the line $9x + 4y = 36$ and the coordinate axes.
A) $13 + \frac{36}{9}$
B) $13 + \frac{36}{\sqrt{97}}$
C) $13 + \frac{36}{10}$
D) $15 + \frac{36}{\sqrt{97}}$
E) $12 + \frac{36}{11}$

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