
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
In a round-robin table tennis tournament with 312 players, each pair of players competes in a match. If player $A_i$ defeats $A_j$, $A_j$ defeats $A_k$, and $A_k$ defeats $A_i$, then the set $\left\{A_i, A_j, A_k\right\}$ is called a triangle. Let $L_i$ and $W_i$ represent the number of matches won and lost by player $A_i$, respectively. It is known that if $A_i$ defeats $A_j$, then $L_i + W_j \geqslant 10$. Find the number of triangles in this round-robin tournament.

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