
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
A five-ring diagram consists of five rings, each with an inner circle diameter of 8 and an outer circle diameter of 10. The small concave quadrilaterals (shaded areas) where the rings intersect pairwise all have equal areas. Given that the total area covered by the five rings is 112.5, find the area of each small concave quadrilateral (use π = 3.14).

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