
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 ball falls from a height $h$ and comes to rest on a horizontal ground after inelastic bounces at a time $t$ from the drop. Assume that during each collision, a given fraction of the ball's mechanical energy is converted into non-mechanical energy. What is this energy loss? The duration of the collisions can be neglected. (Let $h=20 \ \mathrm{cm}$, $t=18 \ \mathrm{s}$, and $g=10 \ \mathrm{m} / \mathrm{s}^{2}$.)

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