
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
Determine the difference in cents between the greatest and least amounts of money that Alicia can have, given that she has $3030$ coins, all of which are either pennies ($1$-cent coins) or nickels ($5$-cent coins), with at least one penny and one nickel.

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