
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
Thirteen tiles are numbered $1$ through $13$. Each of three players randomly selects and keeps three tiles, and sums those tiles. Calculate the probability that all three players obtain an odd sum. Express this probability in lowest terms as $m/n$ and find $m+n$.

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