
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
Sandy plans to paint her daughter's playhouse including two trapezoidal sides of the roof and the front triangular face, all shaded in the diagram. The paint covers 100 square feet per gallon and costs $\$15$ per gallon. The roof sides are each 8 feet wide at the base and 5 feet tall, tapering linearly to a top width of 4 feet. The front face is an equilateral triangle with a 6 feet side. Calculate the total cost of the paint needed.

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