
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
Construct a pigpen with a ground area of 12m² that backs onto a wall. The front of the rectangular pigpen costs half of 12, the cost of the sides is 80 yuan/m², and the roof costs 110 yuan per meter, with no cost for the back of the pigpen. What is the minimum total cost to build the pigpen?

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