
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
Given that a list of five positive integers has a mean of 15 and a range of 24, and the mode and median are both 10, calculate the number of possible different values for the second largest element of the list.

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