
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
Cagney can frost a cupcake every 25 seconds, Lacey can frost a cupcake every 35 seconds, and James can frost a cupcake every 15 seconds. Determine the rate at which Cagney, Lacey, and James can frost cupcakes per second, and then calculate how many cupcakes they can frost in 10 minutes.

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