
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 marble rolls on a horizontal table with a speed  $v_0$ . The marble bounces elastically in a vertical cut at a horizontal distance  $D$  from the edge of the table. After hitting the ground the marble will record a  $x_0$  distance to the edge of the table. $a)$  Determine the equations for horizontal and vertical motion in function of time before hitting the wall. $b)$  Determine the height of the marble at the time of the collision. $c)$  Determine the vertical speed at the instant of the collision. $d)$  Determine the value of  $v_0$  for which  $x_0 = 0$ *Proposed by Danilo Molina, Colon*

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