
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
A small rubber ball moves between two massive vertical walls, colliding with them. One wall is stationary, while the other moves away from it at a constant speed of \( u = 100 \ \text{cm/s} \). Assuming the ball's motion is always horizontal and the collisions are perfectly elastic, find its final speed if the initial speed of the ball was \( v_{0} = 2017 \ \text{cm/s} \).

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