
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 Penniless Pete's piggy bank now has 150 coins consisting of nickels, dimes, quarters, and half-dollars, all totaling $20.00. It does not necessarily contain coins of all four types, calculate the difference between the largest and smallest number of dimes that could be in the bank.

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