
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 ship model with a mass of \(m = 0.5 \,\text{kg}\) is pushed with an initial velocity of \(v = 10 \,\text{m/s}\). The water's resistance force is proportional to the ship model's velocity (\(F = -kv, \, k = 0.5 \,\text{kg/s}\)). Calculate the distance traveled by the ship model:

a) During the time it takes for the velocity to decrease to half,

b) Until it comes to a complete stop!

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