
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
Lisa is constructing a rectangular cardboard box with square bases. She decides that she wants the height of the box to be twice the side length of the square base, plus an additional unit. Determine the smallest possible height of the box if the surface area required is at least 150 square units.

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