
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 student, Theo, needs to earn a total of 30 homework points. For the first six homework points, he has to do one assignment each; for the next six points, he needs to do two assignments each; and so on, such that for every subsequent set of six points, the number of assignments he needs to complete doubles the previous set. Calculate the minimum number of homework assignments necessary for Theo to earn all 30 points.

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