
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 Pete's piggy bank has no pennies in it, but it now contains 120 coins, all nickels, dimes, and half-dollars, with a total value of $10.50. It does not necessarily contain coins of all three types. Determine 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}
user