
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
There are 21 crickets and 30 katydids in a cage. Each time the Red-haired Magician performs, he transforms 2 katydids into 1 cricket. Each time the Green-haired Magician performs, he transforms 5 crickets into 2 katydids. After the two magicians have performed a total of 15 transformations, only katydids remain in the cage. How many katydids are there?

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