
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 asks Chloe to do one homework assignment for each of the first three homework points she wants to earn; for each of the next three homework points, she needs to do two homework assignments; and so on, such that to earn the $n^{\text{th}}$ homework point, she has to do $\lceil n\div3 \rceil$ (rounded up) homework assignments. What is the smallest number of homework assignments necessary to earn a total of 30 homework points?

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