
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
Determine all solutions of the following equation, where \([x]\) is the greatest integer that does not exceed \(x\) (e.g., \([−3.7]=−4\)).

$$
[x]-\sqrt{\frac{[x]}{x-0.5}}-\frac{6}{x-0.5}=0
$$

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