
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 and Lacey can frost a cupcake every 35 seconds. Each takes a 10-second break after every 6 cupcakes they frost. They work together for 10 minutes. Calculate the total number of cupcakes they can completely frost and decorate, including the time it takes to decorate each cupcake.

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