
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
If  $a, b, c$  are real numbers such that  $a+b+c=6$  and  $ab+bc+ca = 9$ , find the sum of all possible values of the expression  $\lfloor a \rfloor + \lfloor b \rfloor + \lfloor c \rfloor$ .

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