
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
[asy] draw((1,0)--(0.309,0.951)--(-0.809,0.588)--(-0.809,-0.588)--(0.309,-0.951)--cycle, black+linewidth(.75)); [/asy]
Debby painted over a pentagonal clock face using the vertex positions to create boundaries. If $t$ is the area of one of the five triangular regions, each bound by two adjacent vertices and the center, and $q$ is the area of the pentagon itself, then calculate $\frac{q}{t}$.
A) $5$
B) $5 \times \frac{\sin(36^\circ)}{\sin(72^\circ)}$
C) $5 \times \frac{\sin(72^\circ)}{\sin(36^\circ)}$
D) $10$

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