
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
Penniless Peggy's piggy bank contains only nickels, dimes, and quarters, amounting to 150 coins in total. The combined value of these coins is $15.00. Peg's bank does not necessarily contain coins of all three types. What is the difference between the largest and smallest number of nickels that could be in the bank?
A) 100
B) 107
C) 113
D) 115
E) 120

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