
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
If the area of $\triangle DEF$ is $100$ square units and the geometric mean between sides $DE$ and $DF$ is $15$ inches, then $\cos E$ is equal to what?
**A)** $\frac{2}{3}$
**B)** $\frac{4}{5}$
**C)** $\frac{\sqrt{17}}{9}$
**D)** $\frac{3}{5}$
**E)** $\frac{1}{2}$

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