
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
How long does a ball dropped from a height $h$ bounce? The coefficient of restitution for the collision between the ground and the ball is represented by $k$. For which types of balls is it useful to measure $k$ in terms of the bounce duration? (The coefficient of restitution is the ratio of the mechanical energy after the collision to the mechanical energy before the collision.)

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