
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 Liam to undertake a challenging homework regimen. For earning each of the first seven homework points, Liam needs to complete three homework assignments; for each of the next seven points, he needs to complete four homework assignments; and so on, such that the number of homework assignments increases by one for every new set of seven points. Calculate the smallest number of homework assignments that Liam needs to complete in order to earn exactly 40 homework points.

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