
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
At Globe Sweets Factory, Alex, Mia, and Jamie are applying glaze to spherical candies. Alex's candies have a radius of 5 mm, Mia's candies have a radius of 7 mm, and Jamie's candies have a radius of 9 mm. The rate at which each worker applies the glaze is proportional to the candy surface area, where Alex’s rate is twice Mia's rate, and Mia’s rate is one and a half times Jamie's rate. Assuming that the glaze has negligible thickness and is distributed equally on all candies, calculate how many candies Alex will have glazed by the first time all three workers finish glazing their current candy at the same time.

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