
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 $R_1R_2R_3R_4R_5$ is a regular pentagon whose apothem (distance from the center to the midpoint of a side) is $5$, and $S_i$ is the midpoint of the side $R_iR_{i+1}$ for $i=1,2,3,4$, then find the area of the quadrilateral $S_1S_2S_3S_4$.
**A)** $10$
**B)** $12.5$
**C)** $15$
**D)** $17.5$
**E)** $20$

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