
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
Bill can buy jags, jigs, and jogs for $\$3$, $\$4$, and $\$10$ each, respectively. What is the largest number of jogs he can purchase if he must buy at least one of each item, the total number of items must be at least 20, and he will spend exactly $\$100$?

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