
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
John, also known for his peculiar choices, is crafting a rectangular storage container with square bases. He prefers the height of the container to be twice the side length of the square base. Determine the minimum height he should use if he wants his container to have a total surface area of at least 150 square units while using the least amount of material possible.

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