
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 another rectangular cardboard box with square bases. This time, she desires the height of the box to be twice the side length of the square base plus 1 unit. If she requires the surface area of the box to be at least 130 square units while using the least amount of cardboard, what should the height be?

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