
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
A math teacher has adjusted the homework policy for Noelle. For the first three homework points, she does not need to do any homework assignments. Starting from the fourth point, for each of the next five homework points, Noelle has to do one homework assignment; for each of the next five points, she needs to do two homework assignments; and so on, so that to earn the $n^{\text{th}}$ homework point, she has to do $(n-3)\div5$ (rounded up) homework assignments. For instance, when she has 11 points, it will take $(12-3)\div5=1.8\rightarrow2$ homework assignments to earn her $12^{\text{th}}$ point. What is the smallest number of homework assignments necessary to earn a total of 25 homework points?

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