
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
Given that Sally has 150 coins consisting only of nickels, dimes, and quarters, totaling $20.00, and the collection contains coins of all three types, determine the difference between the largest and smallest number of nickels that could be in her savings.

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