
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 gray rabbit and a white rabbit set off from their own homes along the same road heading to each other's home. The white rabbit rests every 30 meters, and the gray rabbit rests every 20 meters. They meet at the midpoint and happen to rest simultaneously. If by the time they meet, the gray rabbit has rested 15 more times than the white rabbit, how far apart are their homes in meters?

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