
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 all ordered triples \((a, b, c)\) of positive reals that satisfy: 
\[
\lfloor a\rfloor bc = 3, \quad a\lfloor b\rfloor c = 4, \quad \text{and} \quad ab\lfloor c\rfloor = 5,
\]
where \(\lfloor x\rfloor\) denotes the greatest integer less than or equal to \(x\).

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