
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
Let $\triangle XYZ$ have an area of $81$ square units. The geometric mean (mean proportional) between sides $XY$ and $XZ$ is $15$ inches. If angle $X$ is acute, find the value of $\sin X$.
A) $\frac{9}{25}$
B) $\frac{17}{25}$
C) $\frac{18}{25}$
D) $\frac{3}{5}$
E) $\frac{24}{25}$

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