
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 with mass $m_{1}$, sliding on a smooth horizontal surface, collides with a ball with mass $m_{2}$, which was at rest on the same surface. After the central elastic collision, the balls slide in the same direction, with the speed of the ball with mass $m_{2}$ being four times the speed of the ball with mass $m_{1}$.
1) Find the ratio of the masses $\frac{m_{2}}{m_{1}}$.
2) Find the ratio of the speed of the ball $m_{1}$ before the collision to its speed after the collision.

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