
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
In a photo lab, there are 130 photographs, of which 35 are of the fourth grade, 30 of the fifth grade, 25 of the sixth grade, 20 of the seventh grade, and the rest are from the first through third grades. The photos are mixed and cannot be distinguished by touch. What is the minimum number of photographs that need to be taken, without seeing them, to ensure that among them there are at least 15 from one of the grades from the fourth to the seventh grades?

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