
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
Consider the numbers  $\{24,27,55,64,x\}$ . Given that the mean of these five numbers is prime and the median is a multiple of  $3$ , compute the sum of all possible positive integral values of  $x$ .

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