
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 starts from point \( A \), reflects off a wall located \( 5 \text{ m} \) from \( A \), and reaches point \( B \) which is \( 2 \text{ m} \) from the wall. The ball hits a wall here as well and rolls back to point \( A \). The distance \( AB \) is \( 9 \text{ m} \). The initial speed of the ball is \( v_{0} = 5 \text{ m} \text{ s}^{-1} \), and it has a constant acceleration \( a = -0.4 \text{ m} \text{ s}^{-2} \).

a) With what speed does the ball return to \( A \)?

b) What initial speed would the ball need to have, under the same conditions, to stop exactly at \( A \) upon returning?

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