
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
Cut equal squares from the four corners of a sheet of iron with length $a$ and width $b$ ($0 < b < a$), and then fold it into a lidless rectangular box. If the volume of the circumscribed sphere of this rectangular box has a minimum value, then the range of $\dfrac{a}{b}$ is \_\_\_\_\_\_.

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