
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, Leo, needs to complete homework assignments to earn grades. For the first four grades, he needs to complete one assignment per grade. For the next seven grades, he requires three assignments per grade. For all subsequent grades, the number of homework assignments per grade increases by two for each set of four grades (i.e., he needs 5 assignments per grade for his 12th to 15th grades, 7 assignments for 16th to 19th grades, and so on). Determine the smallest number of homework assignments Leo needs to complete a total of 27 grades.

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