
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
Teacher Zhao took 100 yuan to buy prizes for "Civilized Students". The salesperson told Teacher Zhao: a pencil sharpener costs 15 yuan, 6 notebooks cost 24 yuan, a pencil case costs 5 yuan, and two boxes of colored pencils cost 16 yuan.  
① If only 6 pencil sharpeners are bought, is 100 yuan enough?  
② If 20 notebooks are bought, how many pencil cases can be bought with the remaining money?  
③ Can you propose a mathematical problem? Please solve it.

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