
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
A shipping company charges  $.30l+.40w+.50h$  dollars to process a right rectangular prism-shaped box with dimensions  $l,w,h$  in inches.  The customers themselves are allowed to label the three dimensions of their box with  $l,w,h$  for the purpose of calculating the processing fee.  A customer finds that there are two different ways to label the dimensions of their box  $B$  to get a fee of  $\$ 8.10 $, and two different ways to label $ B $ to get a fee of $ \ $8.70$ .  None of the faces of  $B$  are squares.  Find the surface area of  $B$ , in square inches.

*Proposed by Justin Hsieh*

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