
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
15 balls numerically labeled from 1 to 15 are placed in a bin. Joe produces a list of three numbers by drawing a ball, recording its number, and not replacing it back into the bin. Determine how many different lists of numbers are possible, given that the sum of the three numbers on the list must be even.

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