
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
Find three numbers $a$, $b$, $c$ satisfying $\lfloor a \rfloor + \lfloor b \rfloor = \lfloor a + b \rfloor$, and $\lfloor a \rfloor + \lfloor c \rfloor < \lfloor a + c \rfloor$. (The notation $\lfloor a \rfloor$ represents the greatest integer less than or equal to $a$, known as the floor or integer part of $a$.)

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