
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
Given the set $A=\{(x,y) \,|\, |x| \leq 1, |y| \leq 1, x, y \in \mathbb{R}\}$, and $B=\{(x,y) \,|\, (x-a)^2+(y-b)^2 \leq 1, x, y \in \mathbb{R}, (a,b) \in A\}$, then the area represented by set $B$ is \_\_\_\_\_\_.

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