
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 $20^{\circ}$C temperature, completely inelastic lead ball falls freely from a height of $100 \mathrm{~m}$ onto a solid surface. Assuming all the apparent lost energy is converted into heat absorbed by the ball, answer the following questions:

1. What is the temperature of the ball immediately after the fall?
2. What initial velocity must the ball be given from above to cause its temperature to rise to the melting point of lead?

Given data:
- Specific heat of lead: $C = 0.0315$ (units not specified)
- Mechanical equivalent of heat: $E = 425$ (units not specified)
- Melting point of lead: $T = 335^{\circ}$C
- Gravitational acceleration: $g = 9.80 \frac{\mathrm{m}}{\mathrm{s}^{2}}$

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