
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
20 balls of equal mass and speed move along a trough towards a metal wall. At the same time, 16 balls of the same mass move toward them with the same speed. When two balls collide, they scatter at the same speed. After colliding with the wall, a ball bounces off it with the same speed. (The balls move only along the trough). How many collisions will occur between the balls?

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