
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
100 balls of identical mass and velocities move along a groove towards a metal wall. After colliding with the wall, each ball rebounds off with the same velocity. When two balls collide, they fly apart with the same velocity (the balls move only along the groove). Find the total number of collisions between the balls.

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