
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 the last tile is discarded. The probability that all three players obtain an even sum is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$

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