
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, Lucas, needs to earn 30 homework points. For the first 10 points, each point requires 1 assignment. For the next 10 points, each requires 2 assignments, and for each point beyond the 20th, he needs to do 3 assignments. Calculate the total number of assignments Lucas needs to complete to earn all 30 points.

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