
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
Let P be the number of pennies, N be the number of nickels, and D be the number of dimes. The total value of the coins is $5.00, which gives the equation 0.01P + 0.05N + 0.10D = 5.00. The total number of coins in the bank is 150, giving the equation P + N + D = 150. What is 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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