
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
Ten tiles are numbered $1, 2, 3, \cdots, 10,$ respectively. Each of three players randomly selects and keeps three of the tiles, and sums those three values. The probability that each player obtains an even sum is what we wish to find. Express your final answer as a fraction $m/n$ where $m$ and $n$ are relatively prime positive integers.

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