
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
On a grid paper, where the distance between parallel lines is $1 \mathrm{~cm}$, a circle with a radius of 5 cm is drawn around the intersection point of two grid lines. How many regions are formed that are bordered by both circle arcs and segments of grid lines (and do not contain any segment of a grid line inside them)?

What is the area of each such region?

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