
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
Let  $V$  be a rectangular prism with integer side lengths. The largest face has area  $240$  and the smallest face has area  $48$ . A third face has area  $x$ , where  $x$  is not equal to  $48$  or  $240$ . What is the sum of all possible values of  $x$ ?


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