
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
On a board, the numbers $2, 3, 4, \ldots, 29, 30$ are written. For one dollar, you can mark any number. If a number is already marked, you can mark its divisors and multiples for free. For the smallest amount of dollars, how can you mark all the numbers on the board? [6 points]

(I.V. Yashchenko)

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