
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
For a real number $x$, define $\lfloor x \rfloor$ as the greatest integer less than or equal to $x$, such as $\lfloor 1.5 \rfloor = 1$, $\lfloor 5 \rfloor = 5$, $\lfloor -3.3 \rfloor = -4$. If $\left\lfloor \frac{x+3}{2} \right\rfloor = 3$, then the range of $x$ is ______.

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