
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 greyhound is chasing a rabbit. Initially, the rabbit has a lead of $n$ rabbit hops, and the rabbit makes $a$ hops while the greyhound makes $b$ hops. However, a distance of $d$ greyhound hops is equivalent to $c$ rabbit hops. How many hops can the rabbit make until the dog catches up, and how many hops would the dog have made by then? (For example, if $n=34$, $a=11$, $b=8$, $c=9$, $d=5$, solve the problem for the rabbit's initial lead of $n(=34)$ greyhound hops.)

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