
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
Flash and Arrow decide to race. Flash runs $z$ times as fast as Arrow, where $z > 1$. Arrow gets a head start of $w$ meters. At the signal, they start running in the same direction on a straight track. Arrow has an added advantage such that he maintains his initial lead for $k$ minutes, running at his constant speed before Flash can start reducing the gap. Calculate the distance that Flash must cover to catch up to Arrow assuming they don't stop running.
A) $\frac{zk + w}{z - 1}$
B) $\frac{z(ku + w)}{z - 1}$
C) $\frac{(k + w)z}{z + 1}$
D) $\frac{z(k + w)}{z - 1}$

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