
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
Let  $R$  be the region in the Cartesian plane of points  $(x,y)$  satisfying  $x\geq 0$ ,  $y\geq 0$ , and  $x+y+\lfloor x\rfloor+\lfloor y\rfloor\leq 5$ .  Determine the area of  $R$ .

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